Question

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

Answer 1

Answer:

Option (3)

Step-by-step 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.