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

$\frac{-4d}{-4}= \frac{-16}{-4}$ Divide each sides by - 16.

d = 4

So, d = 4.

Hope this helps yoi!.