Question

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

Answer 1

Answer:

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.

Step-by-step 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.