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

If the first term of a G.P. is 8 and its common ratio is −2 . The 3^rd term of this G.P. is ______.

The 4^th term of a G.P. is 16 and the 7^th term is 128, then its common ratio is equal to ______.

(2x + 2) and (3x + 3) are two consecutive terms of a G.P. The common ratio of the GP. is ______.

The third term of a G.P. is 3. The product of its first five terms is ______.

The 8^th term of a G.P. is 192 and its common ratio is 2, then the first term of the G.P. is ______.

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 next three terms of the sequence :

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

Find the seventh term of the G.P.:

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

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

The sum of first four terms of the G.P. 2, 6, 18, ....., is ______.

The 4^th term of a G.P. is 54 and its 7^th term is 1458, the common ratio of this G.P is ______.

8, x and 32 are in GP., then the value of x is ______.

The sum of three terms (numbers) of a GP. is `3 1/2` and their product is 1; the numbers are ______.

The sum of 20 terms of the G.P. 10, 20, 40, ..... is ______.

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. 

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.

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

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 sum of the first two terms is – 4 and the fifth term is 4 times the third term.

−1, k and −1 are three consecutive terms of a G.P., then 

1. k = 1 
2. k = −1 

Which of the following is valid?

x + 9, 10 and 4 are in GP. The value of x is ______.

The common ratio of a G.P. is 2 and its 6th term is 48. The first term is ______.

Three terms are in G.P., whose product is 27. The middle term is ______.

The common ratio of a GP., whose 4th term is 27 and 6th term is 243; is ______.

The third term of a G.P. = 18, the product of its first five terms is ______.

G.P.: \[\frac{2}{9}, \frac{1}{3}, \frac{1}{2}, \ldots\]. 

Assertion (A): The \[5^{\text{th}}\] term of the given G.P. is \[1\frac{1}{8}\].

Reason (R): If for a G.P., the first term is a, the common ratio is r and the number of terms is n, then the sum of the first n terms is \[S_{n}=\frac{a(r^{n}-1)}{r-1}\] for all r.

For a G.P., its fourth term is x, seventh term is y and tenth term is z. 

Assertion (A): x, y and z are in G.P. 

Reason (R): \[y^{2}=(ar^{6})^{2}=ar^{3}\times ar^{9}=xz\].

Consider the G.P. 3 − 6 + 12 − 24 + ...... − 384. 

Statement (1): The product of the 5^th term from the beginning and the 5^th term from the end is −1152. 

Statement (2): In a G.P., the product of the n^th term from the beginning and the n^th term from the end is the 1^st term + the last term.

The 5^th and the 8^th terms of a G.P. are 32 and 256 respectively. Find its first term and the common ratio.

The third term of a G.P. is greater than its first term by 9 whereas its second term is greater than the fourth term by 18. Find the G.P.

x, 2x + 2, 3x + 3, G are four consecutive terms of a G.P. Find the value of G.

The third term of a G.P. is 2. Find the product of the first five terms of this G.P.

The 10^th, 16^th and 22^nd terms of a G.P. are x, y and z respectively. Show that x, y and z are in GP.

Which term of the GP. 2, 2\[\sqrt{2}\], 4,... is 128\[\sqrt{2}\]?

Find the 8^th term of a GP., if its common ratio is 2 and 10^th term is 768.

In a G.P., the 4^th term is 48 and 7^th term is 384. Find its 6^th term.

`-5/3`, x and `(-3)/5` are three consecutive terms of a G.P. Find the value(s) of x.

Rohit writes a letter to four of his friends. Hе asks each one of them to copy the letter and mail to four different persons with the instructions that they move the chain similarly. Assuming that the chain is not broken and that it costs ₹10 to mail one letter, determine the amount spent on postage when the fourth set of letters is mailed.

The fourth term of a G.P. is eight times its seventh term. The fifth term of then G.P. is `3/16`, then find its 12^th term.

Richard borrows ₹ 10,000 from his friend Ramesh. Ramesh asks him to return the money just by repaying 10 at first day and double the amount in the subsequent days than the each previous day continuously for 10 days. Richard thanks Ramesh for his help. Determine, whether Ramesh was in loss or profit.

The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. A total of 27 flags have to be fixed at intervals of every 3 m. All the flags are kept at the position of the middle most flag. Rohan was given the responsibility of placing the flags on both the sides of the middle most flag. Rohan could carry only one flag at a time. So he carries one flag from the middle most point, places the flag at the designated place and comes back to the middle most point. He continues this for all the flags on both sides.

Based on the above information, answer the following questions:

1. The distance covered by Rohan in placing the flags on one side of the middle most flag forms a sequence. Identify the type of sequence by writing at least the first 4 terms of the sequence.
2. Find the distance covered by Rohan in placing the 10th flag and coming back to the middle most flag.
3. Find the total distance travelled by Rohan in fixing all the 27 flags.