Question

How do you find the term n=12, given the arithmetic sequence `a_1=5` and d=1/3?

Answer 1

`a_12=color(red)(8 2/3)`

Explanation:

The `n^"th"` term, `a_n` of an arithmetic sequence, with initial term, `a_1` and incremental difference `d` is given by the formula:
`color(white)("XXX")a_n=a_1+(n-1)*d`

In this case with `n=12, a_1=5, " and " d=1/3`
`color(white)("XXX")a_12=5+(12-1)*1/3=5+11/3=8 2/3`