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

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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

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