Selina solutions for Mathematics [English] Class 10 ICSE chapter 11 - Geometric Progression [Latest edition]

Find, which of the following sequence from a G.P. :

8, 24, 72, 216, .............

Find, which of the following sequence from a G.P. :

`1/8, 1/24, 1/72, 1/216, ................`

Find, which of the following sequence from a G.P. :

9, 12, 16, 24, ................

Find the 9^th term of the series :

1, 4, 16, 64, ...............

Find the seventh term of the G.P. :

`1, sqrt(3), 3, 3sqrt(3), ............`

Find the 8^th term of the sequence:

`3/4, 1 1/2, 3, ..............`

Find the 10^th term of the G.P. :

`12, 4, 1 1/3, ................`

Find the n^th term of the series :

1, 2, 4, 8, ...............

Find the next three terms of the sequence :

`sqrt5, 5, 5sqrt(5), .............`

Find the sixth term of the series :

2², 2³, 2⁴, ...................

Find the seventh term of the G.P. :

`sqrt(3) + 1, 1, (sqrt(3) - 1)/2, .........`

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

Find the next three terms of the series :

`2/27, 2/9, 2/3, .............`

Find the next two terms of the series :

2 – 6 + 18 – 54 ..........

Which term of the G.P.:

`-10, 5/sqrt(3), -5/6,....` is `-5/72`?

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

Fourth and seventh terms of a G.P. are `1/18` and `-1/486` respectively. Find the G.P.

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

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

Find the geometric progression with 4^th term = 54 and 7^th term = 1458.

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.

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.

If the 4^th and 9^th terms of a G.P. are 54 and 13122 respectively, find the G.P. Also, find its general term.

The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. Show that : q² = pr.

Find the seventh term from the end of the series :

`sqrt(2), 2, 2sqrt(2), ........., 32.`

Find the third term from the end of the G.P.

`2/27, 2/9, 2/3, .........,162.`

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

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

If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.

If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.

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, b², y² are in A.P.

If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `1/x + 1/y = 2/b`

If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `a/x + c/y = 2`

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

Find the sum of G.P. :

1 + 3 + 9 + 27 + .......... to 12 terms. 

Find the sum of G.P. :

0.3 + 0.03 + 0.003 + 0.0003 + ........... to 8 items.

Find the sum of G.P. :

`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms. 

Find the sum of G.P. :

`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.

Find the sum of G.P. :

`(x + y)/(x - y) + 1 + (x - y)/(x + y) + ..........` upto n terms. 

Find the sum of G.P. :

`sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` to n terms. 

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

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.

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

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

A geometric progression has common ratio = 3 and last term = 486. If the sum of its terms is 728; find its first term.

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

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

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.

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

If the sum of 1 + 2 + 2² + ....... + 2^{n – 1} is 255, find the value of n.

Find the geometric mean between `4/9` and `9/4`

Find the geometric mean between 14 and `7/32`

Find the geometric mean between 2a and 8a³

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

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.

Find the 5^th term of the G.P. `5/2, 1, .........`

The first two terms of a G.P. are 125 and 25 respectively. Find the 5^th and the 6^th terms of the G.P.

Find the sum of the sequence `-1/3, 1, -3, 9, ..........` upto 8 terms.

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.

Find a G.P. for which the sum of first two terms is – 4 and the fifth term is 4 times the third term.