Question

For a given arithmetic sequence, the 75th term, a75, is equal to 342, and the 4th term, 24, is equal to - 13.

nd
Find the value of the 32
term, 232

Answer 1

The 32th term is 127.

Explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same. The general equation for an arithmetic sequence is given by:

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

In which d is the common difference.

It can also be written as:

`a_n = a_m + (n - m)d`

75th term is equal to 342, and the 4th term, 24, is equal to - 13.

This means that
`a_4 = -13, a_75 = 342`. We use this to find d. So

`a_(75) = a_4 + (75 - 4)d`

`342 = -13 + 71d`

`71d = 355`

`d = (355)/(71)`

`d = 5`

Find the value of the 32th term:

`a_n = a_m + (n - m)d`

`a_(32) = a_(4) + (32 - 4)d`

`a_(32) = -13 + 28(5) = -13 + 140 = 127`

The 32th term is 127.