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

Write an explicit formula for the sequence and use it to find the eleventh teen in-example-1
User Hakatashi
by
6.5k points

1 Answer

10 votes

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.

User Blase
by
6.3k points
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