{"id":591738,"date":"2022-04-25T05:09:49","date_gmt":"2022-04-25T05:09:49","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=591738"},"modified":"2022-04-25T09:31:17","modified_gmt":"2022-04-25T09:31:17","slug":"selina-class-10-icse-solutions-mathematics-chapter-11-geometric-progression","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/selina-class-10-icse-solutions-mathematics-chapter-11-geometric-progression\/","title":{"rendered":"Selina Class 10 ICSE Solutions Mathematics : Chapter 11-\u00a0Geometric Progression"},"content":{"rendered":"\n

Class 10: Maths Chapter 11 solutions. Complete Class 10 Maths Chapter 11 Notes.<\/p>\n\n\n\n

Selina Class 10 ICSE Solutions Mathematics : Chapter 11- Geometric Progression<\/h2>\n\n\n\n

Selina 10th Maths Chapter 11, Class 10 Maths Chapter 11 solutions<\/p>\n\n\n\n

Exercise 11A<\/h3>\n\n\n\n

Question 1.
Find, which of the following sequence form a G.P. :<\/strong>
(i) 8, 24, 72, 216, \u2026\u2026
(ii) 18,124,172,1216, \u2026\u2026..
(iii) 9, 12, 16, 24, \u2026\u2026
Solution 1(i).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 1(ii).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 1(iii).
<\/strong>\"Selina<\/p>\n\n\n\n

Question 2.
Find the 9th term of the series :
1, 4, 16, 64 \u2026\u2026..
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 3.
Find the seventh term of the G.P. :
1, 3\u2013\u221a, 3, 33\u2013\u221a \u2026..
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 4.
Find the 8th<\/sup> term of the sequence :
34,112 3, \u2026\u2026.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 5.
Find the 10th<\/sup> term of the G.P. :
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 6.
Find the nth<\/sup> term of the series :
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 7.
Find the next three terms of the sequence :
5\u2013\u221a, 5, 55\u2013\u221a, \u2026\u2026
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 8.
Find the sixth term of the series :
22<\/sup>, 23<\/sup>, 24<\/sup>, \u2026\u2026\u2026.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 9.
Find the seventh term of the G.P. :
[late]\\sqrt{3}+1,1, \\frac{\\sqrt{3}-1}{2}[\/latex], \u2026\u2026\u2026\u2026\u2026..
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 10.
Find the G.P. whose first term is 64 and next term is 32.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 11.
Find the next three terms of the series:
227,29,23, \u2026\u2026\u2026\u2026.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 12.
Find the next two terms of the series
2 \u2013 6 + 18 \u2013 54 \u2026\u2026\u2026\u2026
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Exercise 11B<\/h3>\n\n\n\n

Question 1.
Which term of the G.P. :
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 2.
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 3.
Fourth and seventh terms of a G.P. are 118 and \u22121486 respectively. Find the GP.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 4.
If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 5.
The product of 3rd and 8th terms of a G.P. is 243. If its 4th<\/sup> term is 3, find its 7th<\/sup> term.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 6.
Find the geometric progression with 4th<\/sup> term = 54 and 7th<\/sup> term = 1458.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 7.
Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 8.
The fourth term, the seventh term and the last term of a geometric progression are 10, 80 and 2560 respectively. Find its first term, common ratio and number of terms.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 9.
If the 4th and 9th terms of a G.P. are 54 and 13122 respectively, find the GP. Also, find its general term.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 10.
The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. Show that : q2<\/sup> = pr.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Exercise 11C<\/h3>\n\n\n\n

Question 1.
Find the seventh term from the end of the series : 2\u2013\u221a , 2, 22\u2013\u221a, \u2026\u2026\u2026. 32.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 2.
Find the third term from the end of the GP.
227,29,23, \u2026\u2026\u2026\u2026.. 162
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 3.
For the 127,19,13, \u2026\u2026\u2026\u2026 81;
find the product of fourth term from the beginning and the fourth term from the end.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 4.
If for a G.P., pth<\/sup>, qth<\/sup> and rth<\/sup> terms are a, b and c respectively ; prove that :
(q \u2013 r) log a + (r \u2013 p) log b + (p \u2013 q) log c = 0
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 5.
If a, b and c in G.P., prove that : log an<\/sup>, log bn<\/sup> and log cn<\/sup> are in A.P.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 6.
If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 7.
If a, b and c are in A.P. a, x, b are in G.P. whereas b, y and c are also in G.P. Show that : x2<\/sup>, b2<\/sup>, y2<\/sup> are in A.P.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 8.
If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that :
\"Selina
Solution 8(i).<\/strong>
\"Selina<\/p>\n\n\n\n

Solution 8(ii).
<\/strong>\"Selina<\/p>\n\n\n\n

Question 9.
If a, b and c are in A.P. and also in G.P., show that: a = b = c.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 10.
The first term of a G.P. is a and its nth<\/sup> term is b, where n is an even number.If the product of first n numbers of this G.P. is P ; prove that : p2<\/sup> \u2013 (ab)n<\/sup>.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 11.
If a, b, c and d are consecutive terms of a G.P. ; prove that :
(a2<\/sup> + b2<\/sup>), (b2<\/sup> + c2<\/sup>) and (c2<\/sup> + d2<\/sup>) are in GP.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 12.
If a, b, c and d are consecutive terms of a G.P. To prove:
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Exercise 11D<\/h3>\n\n\n\n

Question 1.
Find the sum of G.P. :<\/strong>
(i) 1 + 3 + 9 + 27 + \u2026\u2026\u2026.. to 12 terms.
(ii) 0.3 + 0.03 + 0.003 + 0.0003 + \u2026\u2026 to 8 terms.
\"Selina
Solution 1(i).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 1(ii).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 1(iii).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 1(iv).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 1(v).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 1(vi).
<\/strong>\"Selina<\/p>\n\n\n\n

Question 2.
How many terms of the geometric progression 1+4 + 16 + 64 + \u2026\u2026\u2026 must be added to get sum equal to 5461?
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 3.
The first term of a G.P. is 27 and its 8th<\/sup> term is 181. Find the sum of its first 10 terms.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 4.
A boy spends \u20b9 10 on first day, \u20b9 20 on second day, \u20b9 40 on third day and so on. Find how much, in all, will he spend in 12 days?
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 5.
The 4th and the 7th terms of a G.P. are 127 and 1729 respectively. Find the sum of n terms of this G.P.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 6.
A geometric progression has common ratio = 3 and last term = 486. If the sum of its terms is 728 ; find its first term.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 7.
Find the sum of G.P. : 3, 6, 12, \u2026\u2026\u2026\u2026\u2026. 1536.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 8.
How many terms of the series 2 + 6 + 18 + \u2026\u2026\u2026\u2026.. must be taken to make the sum equal to 728 ?
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 9.
In a G.P., the ratio between the sum of first three terms and that of the first six terms is 125 : 152.
Find its common ratio.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 10.
Find how many terms of G.P. 29\u221213+12 \u2026\u2026\u2026. must be added to get the sum equal to 5572?
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 11.
If the sum 1 + 2 + 22<\/sup> + \u2026\u2026\u2026. + 2n-1<\/sup> is 255, find the value of n.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 12.
Find the geometric mean between :<\/strong>
(i) 49 and 94
(ii) 14 and 732
(iii) 2a and 8a3<\/sup>
Solution 12(i).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 12(ii).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 12(iii).
<\/strong>\"Selina<\/p>\n\n\n\n

Question 13.
The sum of three numbers in G.P. is 3910 and their product is 1. Find the numbers.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 14.
The first term of a G.P. is -3 and the square of the second term is equal to its 4th<\/sup> term. Find its 7th<\/sup> term.
Solution:<\/strong><\/p>\n\n\n\n

\"Selina<\/figure>\n\n\n\n

Question 15.
Find the 5th<\/sup> term of the G.P. 52, 1, \u2026..
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 16.
The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 17.
Find the sum of the sequence \u201313, 1, \u2013 3, 9, \u2026\u2026\u2026\u2026. upto 8 terms.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 18.
The first term of a G.P. in 27. If the 8thterm be 181, what will be the sum of 10 terms ?
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 19.
Find a G.P. for which the sum of first two terms is -4 and the fifth term is 4 times the third term.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Additional Questions<\/strong><\/p>\n\n\n\n

Question 1.
Find the sum of n terms of the series :<\/strong>
(i) 4 + 44 + 444 + \u2026\u2026\u2026
(ii) 0.8 + 0.88 + 0.888 + \u2026\u2026\u2026\u2026..
Solution 1(i).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 1(ii).
<\/strong>\"Selina<\/p>\n\n\n\n

Question 2.
Find the sum of infinite terms of each of the following geometric progression:
\"Selina<\/strong>
\"Selina
Solution 2(i).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 2(ii).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 2(iii).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 2(iv).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 2(v).
<\/strong>\"Selina<\/p>\n\n\n\n

Question 3.
The second term of a G.P. is 9 and sum of its infinite terms is 48. Find its first three terms.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 4.
Find three geometric means between 13 and 432.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 5.
Find :<\/strong>
(i) two geometric means between 2 and 16
(ii) four geometric means between 3 and 96.
(iii) five geometric means between 359 and 4012
Solution 5(i).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 5(ii).
<\/strong>\"Selina<\/p>\n\n\n\n

Solution 5(iii).
<\/strong>\"Selina<\/p>\n\n\n\n

Question 6.
The sum of three numbers in G.P. is 3910 and their product is 1. Find the numbers.
Solution:<\/strong>
Sum of three numbers in G.P. = 3910 and their product = 1
Let number be ar, a, ar, then
\"Selina
\"Selina<\/p>\n\n\n\n

Question 7.
Find the numbers in G.P. whose sum is 52 and the sum of whose product in pairs is 624.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 8.
The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Download PDF<\/strong><\/h2>\n\n\n\n

Selina Class 10 ICSE Solutions Mathematics : Chapter 11- Geometric Progression<\/p>\n\n\n\n

Download PDF<\/strong>: Selina Class 10 ICSE Solutions Mathematics : Chapter 11-\u00a0Geometric Progression PDF<\/a><\/p>\n\n\n\n

Chapterwise Selina Publishers ICSE Solutions for Class 10 Maths :<\/strong><\/h2>\n\n\n\n