# ICSE Solutions for Selina Concise Chapter 11 Geometric Progressions Class 10 Maths

**Exercise 11(A)**

**1. ****Find, which of the following sequence form a G.P. :**

**(i) 8, 24, 72, 216, ….****(ii) 1/8,1/24,1/72,1/216, ……****(iii) 9, 12, 16, 24, …****Solution **

(i)

(ii)

(iii)

**2. ****Find the 9th term of the series :****1, 4, 16, 64 …****Solution**

**3. ****Find the seventh term of the G.P. :****1, ****√****3, 3, 3****√****3…..**

**Solution**

**4. ****Find the 8 ^{th} term of the sequence :**

**34,112 3, ……**

**Solution**

**5. ****Find the 10 ^{th} term of the G.P. :**

**Solution**

**6. ****Find the n ^{th} term of the series :**

**Solution**

**7. ****Find the next three terms of the sequence :****√****5, 5, 5****√****5, ……**

**Solution**

**8. ****Find the sixth term of the series :****2 ^{2}, 2^{3}, 2^{4}, ……**

**Solution**

**9. ****Find the seventh term of the G.P. :****√3+1, 1, (√3−1)/2, ……****Solution**

**10. ****Find the G.P. whose first term is 64 and next term is 32.****Solution**

**11. ****Find the next three terms of the series:****2/27,2/9,2/3, ……****Solution**

**12. ****Find the next two terms of the series****2 – 6 + 18 – 54 ……****Solution**

**Exercise 11(B)**

**1. ****Which term of the G.P. : ****− 10, 5/√3, −5/6,……. is −5/72 ?****Solution**

**2. ****The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.****Solution**

**3. ****Fourth and seventh terms of a G.P. are 1/18 and −1/486 respectively. Find the GP.****Solution**

**4. ****If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term.****Solution**

**5. ****The product of 3rd and 8th terms of a G.P. is 243. If its 4 ^{th} term is 3, find its 7^{th} term.**

**Solution**

**6. F****ind the geometric progression with 4 ^{th} term = 54 and 7^{th} term = 1458.**

**Solution**

**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**

**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**

**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**

**10. ****The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. Show that : q ^{2} = pr.**

**Solution**

**Exercise 11(C)**

**1. ****Find the seventh term from the end of the series : ****√****2, 2, 2****√****2, …. 32.**

**Solution**

**2. ****Find the third term from the end of the GP.****2/27, 2/9, 2/3, …… 162**

**Solution**

**3. ****For the 1/27,1/9,1/3, …… 81;****find the product of fourth term from the beginning and the fourth term from the end.**

**Solution**

**4. ****If for a G.P., p ^{th}, q^{th} and r^{th} terms are a, b and c respectively ; prove that :**

**(q – r) log a + (r – p) log b + (p – q) log c = 0**

**Solution:**

**5. ****If a, b and c in G.P., prove that : log a ^{n}, log b^{n} and log c^{n} are in A.P.**

**Solution**

^{2}= ac

^{2}) = log(ac)

**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**

**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 : x ^{2}, b^{2}, y^{2} are in A.P.**

**Solution**

**8. ****If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that :****(i) 1/x + 1/y = 2/b(ii) a/x + c/y = 2**

**Solution**

(i)

(ii)

**9. ****If a, b and c are in A.P. and also in G.P., show that: a = b = c.**

**Solution**

**10. ****The first term of a G.P. is a and its n ^{th} term is b, where n is an even number.If the product of first n numbers of this G.P. is P ; prove that : p^{2} – (ab)^{n}.**

**Solution**

**11. ****If a, b, c and d are consecutive terms of a G.P. ; prove that :****(a ^{2} + b^{2}), (b^{2} + c^{2}) and (c^{2} + d^{2}) are in GP.**

**Solution**

**12. ****If a, b, c and d are consecutive terms of a G.P. To prove:****1/(a ^{2} + b^{2}), 1/(b^{2} + c^{2}) and 1/(c^{2} + d^{2}) are in G.P.**

**Solution**

**Exercise 11(D)**

**1.**

**Find the sum of G.P. :**

**(i) 1 + 3 + 9 + 27 + ……. to 12 terms.**

**(ii) 0.3 + 0.03 + 0.003 + 0.0003 + …… to 8 terms.**

**(iii) 1 −1/2 + 1/4 −1/8 + ……. to 9 terms.**

**(iv) 1 −1/3 + 1/3 ^{2} −1/3^{2} + ……. to n terms.**

**(v) (x+y)/(x-y) + 1 + (x-y)/(x+y) + ……. upto n terms.**

**(vi) √3 +1/√3 + 1/3√3 + ……. to n terms.**

**Solution**

(i)

(ii)

(iii)

(iv)

(v)

(vi).

**2. ****How many terms of the geometric progression 1+4 + 16 + 64 + ……… must be added to get sum equal to 5461?**

**Solution**

**3. ****The first term of a G.P. is 27 and its 8 ^{th} term is 1/81. Find the sum of its first 10 terms.**

**Solution**

**4. ****A boy spends ₹ 10 on first day, ₹ 20 on second day, ₹ 40 on third day and so on. Find how much, in all, will he spend in 12 days?**

**Solution**

**5. ****The 4th and the 7th terms of a G.P. are 1/27 and 1/729 respectively. Find the sum of n terms of this G.P.**

**Solution**

**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**

**7. ****Find the sum of G.P. : 3, 6, 12, …... 1536.**

**Solution**

**8. ****How many terms of the series 2 + 6 + 18 + …... must be taken to make the sum equal to 728 ?**

**Solution**

**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**

**10. ****Find how many terms of G.P. 2/9−1/3+1/2 ………. must be added to get the sum equal to 55/72?**

**Solution**

**11. ****If the sum 1 + 2 + 2 ^{2} + ……. + 2^{n-1} is 255, find the value of n.**

**Solution**

**12. ****Find the geometric mean between :****(i) 4/9 and 9/4****(ii) 14 and 7/32****(iii) 2a and 8a ^{3}**

**Solution**

(i)

(ii)

(iii)

**13. ****The sum of three numbers in G.P. is 39/10 and their product is 1. Find the numbers.**

**Solution**

**14. ****The first term of a G.P. is -3 and the square of the second term is equal to its 4 ^{th} term. Find its 7^{th} term.**

**Solution**

**15. ****Find the 5 ^{th} term of the G.P. 5/2, 1, …..**

**Solution**

**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**

**17. ****Find the sum of the sequence –1/3, 1, – 3, 9, …… upto 8 terms.****Solution**

**18. ****The first term of a G.P. in 27. If the 8thterm be 1/81, what will be the sum of 10 terms ?****Solution**

**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**

**Additional Questions**

**1. ****Find the sum of n terms of the series :****(i) 4 + 44 + 444 + ……****(ii) 0.8 + 0.88 + 0.888 + ……**

**Solution**

(i)

(ii)

**2. ****Find the sum of infinite terms of each of the following geometric progression:****(i) 1+ 1/3 + 1/9 + 1/27 + ……(ii) 1 – 1/2 + 1/4 – 1/8 + ……. (iii) 1/3 + 1/3**

^{2}– 1/3

^{3}+ ……(iv) √2 – 1/√2 + 1/2√2 – 1/4√2 + ……(v) √3 + 1/√3 + 1/3√3 + 1/9√3 + ……..

**Solution**

(i)

(ii)

(iii)

(iv)

(v)

**3. ****The second term of a G.P. is 9 and sum of its infinite terms is 48. Find its first three terms.**

**Solution**

**4. ****Find three geometric means between 13 and 432.**

**Solution**

**5. ****Find :****(i) two geometric means between 2 and 16****(ii) four geometric means between 3 and 96.****(iii) five geometric means between 3(5/9) and 40(1/2)**

**Solution **

(i)

(ii)

(iii).

**6. ****The sum of three numbers in G.P. is 39/10 and their product is 1. Find the numbers.**

**Solution**

Sum of three numbers in G.P. = 39/10 and their product = 1

Let number be a/r, a, ar, then

**7. ****Find the numbers in G.P. whose sum is 52 and the sum of whose product in pairs is 624.**

**Solution**

**8. ****The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.**