Question

What is the closed linear form of the sequence 3, 4, 5, 6, 7, ...?

A) an = 2 + n
B) an = 2 - n
C) an = 3 + n
D) an = 3 - n

Answer 1

Explanation:

This is an arith. sequence.

The first term is 3 and the common difference is 1

Thus, the general formula for the nth term of this sequence is:

a(n) = 3 + 1(n - 1) This matches Answer A

Answer 2

`a_n=2+ n`

EXPLANATION

The given sequence has terms:

3, 4, 5, 6, 7, ...

The first term is

`a_1=3`

The constant difference is

d=4-3=1

The general term is given by:

`a_n=a_1 + d(n - 1)`

Substitute the first term and the common difference to get,

`a_n=3+ 1(n - 1)`

Expand:

`a_n=3+ n - 1`

`a_n=2+ n`

The first choice is correct.