Question

The sum of the first 10 terms of an arithmetic progression is 40. If the first term is -5, then what is the common difference?-3-124

Answer 1

Given data:

The sum of the first 10 terms of an arithmetic progression = 40

The first term is -5

Using the formula to get the sum of an arithmetic term

$S_n=\frac{n}{2}\lbrack2a+(n-1)d\rbrack$

from the above formula

$\begin{gathered} a=-5 \\ n=10 \\ S_n=40 \\ d\text{ is unknown} \end{gathered}$

Method: substitute the values and make d the subject of the formula

$40=\frac{10}{2}\lbrack2\times-5+(10-1)\times d\rbrack$

=>

$40=5(-10+9d)$

=> divide both sides by 5

$\frac{40}{5}=\frac{5(-10+9d)}{5}$

=>

$8=-10+9d$

=> collect like terms

9d=10+8

=>

9d=18

=>Divide both sides by 9

$d=\frac{18}{9}=2$

Therefore the common difference is 2