Question

Given the explicit formula for a geometric sequence find the first five terms and the 8th term an = 2.(1/4)^n,_1

Answer 1

An = 2×(1/4)^n

First five terms are
A1 = 2×(1/4)^1 = 2×(1/4) = 1/2
A2 = 2×(1/4)^2 = 2×(1/16) = 1/8
A3 = 2×(1/4)^3 = 2×(1/64) = 1/32
A4 = 2×(1/4)^4 = 2×(1/256) = 1/128
A5 = 2×(1/4)^5 = 2×(1/1024) = 1/512

8th term is
A8 = 2×(1/4)^8 = 2×(1/65536) = 1/32768

Answer 2

The an term is given by an=2x(1/4)n
For first term put n=1
a1=2x(1/4)=1/2
For 2nd term put n=2
a2=2x(1/4)²=2x1/16=1/8
For 3rd term put n=3
a3=2x(1/4)³=2x(1/64)=1/32
For 4th term
a4=2x(1/4)^4=2x1/256=1/128
For 5th term ,put n=5
a5=2x(1/4)^5=2x(1/1024)=1/512

For 8th term put n=8
a8=2x(1/4)^8=1/32768