Question

Find the sum of the first seven terms of the sequence 4, 12, 36, 108, … .

a. 1,456B.1,457C.4,372D.4,374

Answer 1

The given sequence is 4,12,36,108....

Here we can observe the first term
`a_(1)` = 4 ,
`a_(2)=12` and so on.

The common ratio (r)=
`(12)/(4)=3`

Since the common ratio is greater than 1,

Therefore the sum of the geometric series =
`(a(r^(n)-1))/(r-1)`

Since we have to find the sum of first seven terms, so n=7

=
`(4(3^(7)-1))/(3-1)`

=4372.

Therefore, option C is the correct answer.