Question

Given the formula for the nth term, state the first 5 terms of each sequence.tn=1/2(2)^n-1

Answer 1

Given,

The expression is,

`t_n=(1)/(2)(2)^(n-1)`

Required

The first five term of the sequence.

Taking n= 1 then,

`t_1=(1)/(2)(2)^(1-1)=(1)/(2)`

Taking n= 2 then,

`t_2=(1)/(2)(2)^(2-1)=(1)/(2)*2=1`

Taking n= 3 then,

`t_3=(1)/(2)(2)^(3-1)=(1)/(2)*4=2`

Taking n= 4 then,

`t_4=(1)/(2)(2)^(4-1)=(1)/(2)*8=4`

Taking n= 5 then,

`t_5=(1)/(2)(2)^(5-1)=(1)/(2)*16=8`

Hence, the first five term of the sequence is 1/2, 1,2, 4, 8.