GP J1

 

The 1st term of a geometric progression is 2 and the 5th term is 512. Find the common ratio.

 

Solution

 

G₁=2, G₅=512, n=5

 

G_n = G₁r^n-1;

 

G₅ = G₁r^5-1;

 

G₅ = G₁r⁴;

 

512 = 2 x r⁴;

 

512 = 2r⁴;

 2       2

 

256 = r⁴;  Finding the fourth root of 256,

We do prime factorization of 256.

 

2	256
2	128
2	64
2	32
2	16
2	8
2	4
2	2
	1

 

 

 

 

 

 

 

 

 

 

 

4⁴ = r⁴;  [equal powers will cancel out]

 

4 = r

 

r = 4

 

 

Hence the common ratio is 4.

 

TRY THIS …………..

The 1st term of a geometric progression is 3 and the 5th term is 9375. Find the common ratio.