Question

Position
1 2 3 4 5 n
Value of term
2 12 17 22 27

Answer 1

Note: It seems the first term of your sequence is 7 instead of 2. So, I am assuming you meant the sequence such as;

7, 12, 17, 22, 27

Answer:

The expression for the nth term of the givens sequence is:

• 
  `a_n=5n+2`

Explanation:

Given the sequence

7, 12, 17, 22, 27

Here, the first element of the sequence is:

`a_1=7`

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

`12-7=5,\:\quad \:17-12=5,\:\quad \:22-17=5,\:\quad \:27-22=5`

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

`d=5`

so substituting d = 5 and
`a_1=7` in the nth term to determine the expression

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

`a_n=5\left(n-1\right)+7`

`a_n=5n+2`

Therefore, the expression for the nth term of the givens sequence is:

• 
  `a_n=5n+2`