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Daniel [21]
3 years ago
9

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

Mathematics
1 answer:
ki77a [65]3 years ago
3 0

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.

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