Question

What is D of the arithmetic sequence for which a5 equals 24 and a9 equals 40

Answer 1

In an arithmetic sequence d represent the common difference.

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

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

Where
`a_(n)`= nth term and

`a_(1)` = First term.

Given,
`a_(5) = 24, a_(9) = 40`. Therefore,

`a_(1) +(5-1)d = 24 , a_(1) +(9-1)d = 40`

`a_(1) +4d = 24 , a_(1) +8d = 40`

Next step is to subtract the above equations so that we can eliminate a1 and get the value of d. Hence,

4d - 8d = 24 - 40

-4d = - 16

`(-4d)/(-4)= (-16)/(-4)` Divide each sides by - 16.

d = 4

So, d = 4.

Hope this helps yoi!.