# HOW TO FIND THE GEOMETRIC PROGRESSION WITH GIVEN INFORMATION

How to Find the Geometric Progression with Given Information ?

Here we are going to see some practice questions of finding geometric progression with given information.

## How to Find the Geometric Progression with Given Information - Questions

Question 1 :

In a G.P. the 9th term is 32805 and 6th term is 1215. Find the 12th term.

Solution :

 9th term is 32805t9  = 32805ar8  =  32805   -----(1) 6th term is 1215t6  = 1215ar5  =  1215  -----(2)

(2) / (1)  ==> ar5/ar8  =  1215/32805

1/r3  =  1/27

(1/r)3  =  (1/3)3

r = 3

By applying the value of r in (2), we get

a(3)5  =  1215

a  =  1215/35

a  =  5(35)/35

a = 5

12th term :

t12  =  ar11

t12   =  5(3)11

Question 2 :

Find the 10th term of a G.P. whose 8th term is 768 and the common ratio is 2.

Solution :

8th term is 768

t8  =  768

ar7  =  768

r = 2

a(27)  =  768

a  =  768/128

a = 6

10th term :

t10  =  ar9

=  6(29)

=  6(512)

t10  =  3072

Hence the 10th term of the sequence is 3072.

Question 3 :

If a, b, c are in A.P. then show that 3a, 3b, 3c are in G.P.

Solution :

If a, b, c are in A.P, then b = (a + c)/2

In G.P,  b  =  √ac

To prove that 3a, 3b, 3c are in G.P.

3b  =  √(3⋅ 3c

3b  =  (3a + c)1/2

3b  3(a+c)/2

b = (a + c)/2

Hence 3a, 3b, 3c are in G.P.

Question 4 :

In a G.P. the product of three consecutive terms is 27 and the sum of the product of two terms taken at a time is 57/2 . Find the three terms.

Solution :

Let the three terms be a/r, a, ar

The product of three consecutive terms  =  27

(a/r)  a  ar  =  27

a3  =  27

a  =  3

Sum of the product of two terms taken at a time  =  57/2

[(a/r)  a] + [ ar] + [ar  a/r]  =  57/2

a2/r + a2r + a2  =  57/2

a2(1/r + r + 1)  =  57/2

9(1 + r + r2)/r  =  57/2

18(r2 + r + 1)  =  57 r

18r+ 18r + 18  =  57 r

18r+ 18r - 57r + 18  =  0

18r - 39r + 18  =  0

6r - 13r + 6  =  0

(2r - 3)(3r - 2)  =  0

r = 3/2 and r = 2/3

First term  =  a/r  =  3/(3/2)  =  2

Second term  =  a  =  3  =  3

Third term  =  ar  =  3(3/2)  =  9/2

Hence the required three terms are 2, 3, 9/2 (or) 9/2, 3, 2.

After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Geometric Progression with Given Information".

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