Question

A sequence is defined by the explicit formula an=3n+4 Which recursive formula represents the same sequence of numbers?

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Answer 1

C

Explanation:

i took the test

Answer 2

Option (3)

Explanation:

Explicit formula of the sequence is,

`a_n=3^n+4`

From this explicit formula,

First term of the sequence will be,

`a_1=(3^1)+4`

`a_1=7`

Second term of the sequence,

`a_2=(3^2)+4`

`a_2` = 13

3rd term of the sequence,

`a_(3)=(3^3)+4`

= 31

Sequence formed,

7, 13, 31 ..........

From the given options,

Recursive formula,

`a_n=3a_(n-1)-8`

`a_2=3(a_1)-8`

`a_2=3(7)-8`

`a_2=21-8` = 13

`a_3=3a_2-8`

`a_3=3a_2-8`

`a_3=3(13)-8`

= 39 - 8

= 31

Sequence formed from this recursive formula will be,

7, 13, 31........

Therefore, Option (3) will be the answer.