Question

What is the 32nd term of the arithmetic sequence where a1 = 4 and a6 = 24?

Answer 1

32nd term `a_32 = 128`

Explanation:

If `a_1` is first term, `d` is the common difference, and `a_n` is the `nth` term of an arithmetic sequence, then relationship between these is

`a_n = a_1 + (n – 1)d`

To find `d`, plug-in the given values
`a_6 = a_1 + (6 – 1)d`
`24 = 4 + (6 – 1)d`
Solving for `d` we obtain
`5d=20`
or `d=4`

To find 32nd term, plug-in appropriate values
`a_32 = 4 + (32 – 1)4`
`a_32 = 128`