Find an explicit formula for the arithmetic sequence -11,-3,5,13,...

Question

I struggle with problems like these for whatever reason and with arithmetic sequence it's confusing to me. I would though prefer to get an set by step of what to do in the problem as well as an explanation to get the answer. Thanks in advance. I just tend to struggle in problems like these and I don't understand it.

Answer 1

The explicit formula for the nth term of an arithmetic sequence is a(n) = a(1) + (n-1)*d where:

a(n) is the nth term

a(1) is the 1st term

n is the number of terms

and d is the constant difference between terms

Looking at the given sequence, we can see that each number is 8 greater than the previous number so d = 8.

a(1) = -11.

so the equation becomes a(n) = -11 + (n-1)8

a(n) = -11 + 8n - 8

a(n) = -19 + 8n