GEOMETRICAL PROGRESSION 1

The 1st term of a geometric progression is 5 and the 7th term is 320. Find the common ratio.

solution

G₁=5, G₇=320, n=7

G_n = G₁r^n-1;

G₇ = G₁r^7-1;

G₇ = G₁r⁶;

320 = 5 x r⁶;

320 = 5r⁶;

 5      5

64 = r⁶;  Finding the 6th root of 64,

r = 2

Hence the common ratio is 2.

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The 1st term of a geometric progression is 2 and the 6th term is 324. Find the common ratio.