Question

Find the 100th AND the nth term for the following sequence. Please show work.

a. 197+7 x 3^27, 197+8 x 3^27, 197+9 x 3^27

Answer 1

The 100th term is
`a_(100)=197+106.3^(27)`

The nth term is
`a_n=197+(n+6).3^(27)`

Explanation:

Forming the sequence we see that

`a_1=197+7.3^(27)=197+(1+6).3^(27)`

`a_2=197+8.3^(27)=197+(2+6).3^(27)`

`a_3=197+9.3^(27)=197+(3+6).3^(27)`

Evidently,

`a_n=197+(n+6).3^(27)`

So,

`a_(100)=197+106.3^(27)`