Question

How do you find the 18th term of the arithmetic sequence in which `a_1 = 3` and `d = 7`?

Answer 1

`122`

Explanation:

An arithmetic sequence is a sequence where there is a common difference that is added on from the last term. The natural numbers (`1,2,3,4..`) are an arithmetic sequence with a common difference of `1`. This is written

`a_n=a_(n-1)+1`

Finding the `n`th term of an arithmetic sequence given the first term and the common difference is done by taking the first term and adding on `n-1` common differences, or

`a_n=a_1+(n-1)d`

where `n` is the number term it is, in this case `18`.

You can make sense of this because the first term has no common difference, the second term has one, the third term has two, and so on,

`a_1=a_1+0d`
`a_2=a_1+1d`
`a_3=a_1+2d`
`a_4=a_1+3d`, etc,

each time the coefficient in front of `d` is one less than the number term it is.

We are given in the question that `a_1` is 3 and `d` is 7, so

`a_18=3+(18-1)*7`

`=3+17*7=122`