Question

if the second term an the sixth term of a geometric sequence are 4 and 1/4 respectively, find the 8th term

Answer 1

The nth term of a G.P. series is given by:
$a_{n}$=a₁rⁿ⁻¹ where a₁ is the first term of the series and r is the common ratio.
By the given question, a₂=a₁r²⁻¹=a₁r=4 ----(1) and
a₆=a₁r⁶⁻¹=a₁r⁵=1/4 ----(2)
dividing (2) by (1) we get,
a₁r⁵/a₁r=(1/4)/4
or, r⁴=1/16
or, r⁴=1/2⁴
or, r=1/2
∴, a₁=4/r [using (1)]
         =4/(1/2)
         =4×2
         =8
∴, a₈=a₁r⁸⁻¹=8r⁷=8×(1/2⁷)=8/128=1/16