Question

For the sequence an = 2n + 1, identify the values of a0 = _____, a1 = _____, a2 = _____, and a3 = _____.

A) a0 = 2, a1 = 3, a2 = 5, and a3 = 9

B) a0 = 1, a1 = 2, a2 = 4, and a3 = 7

C) a0 = 2, a1 = 4, a2 = 5, and a3 = 7

D) a0 = 2, a1 = 3, a2 = 4, and a3 = 6

Answer 1

Option A -
`a_0= 2,a_1= 3,a_2= 5,a_3= 9`

Explanation:

Given : For the sequence
`a_n= 2^n + 1`

To find : Identify the values of following?

Solution :

The nth term of the sequence is
`a_n= 2^n + 1`

Substitute n=0,1,2 and 3

When n=0,

`a_0= 2^0+ 1`

`a_0= 1+1`

`a_0=2`

When n=1,

`a_1= 2^1+ 1`

`a_1= 2+1`

`a_1=3`

When n=2,

`a_2= 2^2+ 1`

`a_2=4+1`

`a_2=5`

When n=3,

`a_3= 2^3+ 1`

`a_3= 8+ 1`

`a_3= 9`

Therefore, The value is
`a_0= 2,a_1= 3,a_2= 5,a_3= 9`

So, Option A is correct.