Question

Use the explicit formula
`a_n=a_1(n-1)*d` to find the 500th term of the sequence below.

24, 30, 36, 42, 48, ...

Answer 1

The correct formula to find the general term of an arithmetic sequence is,

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

Where ,
`a_(n)` = nth term.

`a_(1)`= First term

and d = common difference.

The given sequence is: 24, 30, 36, 42, 48, ...

Here
`a_(1)`= 24,

d = 30-24 = 6

We need to find the 500th term. So, n = 500.

Next step is to plug in these values in the above formula. Therefore,

`a_(500) =24 +(500-1)*6`

= 24 + 499 * 6

= 24 + 2994

= 3018

Therefore, 500th of this sequence is 3018.

Hope this helps you!