Question

What expression can be used to find the nth term in the sequence 5,7,9, 11,...?

2n - 3

n + 2

n - 3

2n + 3​

Answer 1

The required expression which can be used to find the nth term in the sequence is:

`a_n=2n+3`

Hence, the fourth option i.e. 2n+3 is the correct option.

Explanation:

Given the sequence

5, 7, 9, 11,...

An arithmetic sequence has a constant difference 'd' and is defined by

`a_n=a_1+\left(n-1\right)d`

computing the differences of all the adjacent terms

`7-5=2,\:\quad \:9-7=2,\:\quad \:11-9=2`

The difference between all the adjacent terms is the same and equal to

d = 2

So

• a₁ = 5

• d = 2

Thus, the nth term of the sequence is

`a_n=a_1+\left(n-1\right)d`

substitute a₁ = 5 and d = 2 in the sequence

`a_n=2\left(n-1\right)+5`

`a_n=2n+3`

Therefore, the required expression which can be used to find the nth term in the sequence is:

`a_n=2n+3`

Hence, the fourth option i.e. 2n+3 is the correct option.