Question

Write an explicit formula for the sequence and use it to find the eleventh teen in the sequence.

Answer 1

Given:

The sequence is 2, 4, 8, 16,... .

To find:

The explicit formula for the sequence and use it to find the eleventh teen in the sequence.

Solution:

We have,

2, 4, 8, 16,...

It is a GP because the ratio between two consecutive terms are same..

Here,

First term:
`a = 2`

Common ratio:
`r=(a_2)/(a_)`

`r=(4)/(2)`

`r=2`

The explicit formula of GP is:

`a_n=ar^(n-1)`

Putting
`a=2,r=2`, we get

`a_n=2(2)^(n-1)`

Put n=11 to find the 11th term of the given sequence.

`a_(11)=2(2)^(11-1)`

`a_(11)=2(2)^(10)`

`a_(11)=2(1024)`

`a_(11)=2048`

Therefore, the correct option is D.