The 4th term of a G.P. is 16 and the 7th term is 128

Algebra (10)

The 4^th term of a G.P. is 16 and the 7^th term is 128. Find the first term and common ratio of the series.

Answer

Let a be the first term and r the common ratio and T₄ = 16, T₇ = 128

∴ a r^{4 – 1} = 16 and a r^{7 – 1} = 128

a r³ = 16                 a r⁶ = 128

$\frac{ar6}{ar3}$ = $\frac{128}{16}$

∴ r³ = 8 = 2³

ar³ = 16 ⇒ a × 2³ = 16

∴ a = 2