GEOMETRIC PROGRESSION 1

The 1st term of a geometric progression is 7 and the 7th term is 448. Find the 10^th term.

Solution

G₁=7, G₇=448, n=7

G_n = G₁r^n-1;

G₇ = G₁r^7-1;

G₇ = G₁r⁶;

448 = 7 x r⁶;

448 = 7r⁶;

 7       7

64 = r⁶;  Finding the sixth root of 16,

r = 2

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Now the 10^th term;

G_n = G₁r^n-1;

G₁₀ = G₁r^10-1;

G₁₀ = G₁r⁹;  [G₁ =7, r=2]

G₁₀ = 7 x 2⁹;

G₁₀ = 7 x 512;

Hence G₁₀ =3584

Hence the 10^th term is 3584.

TRY THIS………………………….. 

The 1st term of a geometric progression is 5 and the 6th term is 1215. Find the 8^th term.