Question

The sum of $10$ numbers is $100$. The first term is $1$. Find its common difference.

• A. $2$
• B. $1$
• C. $3$
• D. $4$

Answer 1

Answer: (A)

$2$

The sum of first $n$ terms of arithmetic series formula can be written as,

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$ ............ (1)

$n=$ number of terms $=10$

$S_n=100$

First term, $a=1$

Common difference, $d=?$

From $\left(1\right)$, we have

$100=\frac{10}{2}[2\times 1+(10-1\left)d\right]$

$100=5[2+9d]$

$100=10+45d$

$100-10=45d$

$90=45d$

$d=\frac{90}{45}=2$

The common difference is $2$.