Question

What is the 32nd term of 311, 305, 299

Answer 1

503

Explanation:

For an arithmetic sequence, the n-th term is found by

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

To find
`d` (the common difference) we can simply subtract one of the terms by the last, for example:

`d = 299 - 305 \\d = -6 \\`

The common difference must be the same throughout the entire sequence, so we can do it once more just to be sure:

`d = 305 - 311\\d = -6`

We also have to know that
`a_1` stands for the first term of the sequence, which in this case is 311.

Now that we know this, let's find the 32nd term

`a_(32) = 311 + (32 - 1)-6\\a_(32) = 311 + 192\\a_(32) = 503`

Good luck!

Answer 2

`a_(32)` = 125

Explanation:

d = - 6

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

`a_(32)` = 311 + (32 - 1)( - 6) = 125