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: $r=\dfrac{a_2}{a_}$

$r=\dfrac{4}{2}$

$r=2$

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.