Question

How do you write a rule for the nth term of the arithmetic sequence given d=2, `a_1=5`?

Answer 1

`a_n=2n+3`

Explanation:

The terms in the standard `color(blue)"Arithmetic sequence"` are

`a,a+d,a+2d,a+3d, ...... ,a+(n-1)d`

where a is the 1st term, d, the common difference and the nth term is a + (n -1)d

Each term in the sequence is obtained by adding d to the previous term.

Using the nth term, that is a + (n -1)d

with a = 5 and d = 2

`rArra_n=5+2(n-1)=5+2n-2=2n+3`