Question

The sum of the first $10$ terms of an arithmetic progression is four times the sum of its first five terms. Find the ratio of the first term to the common difference

• A. $1:4$
• B. $4:1$
• C. $2:1$
• D. $1:2$

Answer 1

Answer: (D)

$1:2$

Given:

Sum of first 10 terms $=\frac{10}{2}[2a+(10-1\left)d\right]$

Sum of first 5 terms $=\frac{5}{2}[2a+(5-1\left)d\right]$

$\therefore$ According to problem

$\Rightarrow \frac{10}{2}[2a+(10-1\left)d\right]=4.\frac{5}{2}[2a+(5-1\left)d\right]$

$\Rightarrow 2a+9d=4a+8d$

$\Rightarrow 2a=d$

$\Rightarrow a:d=1:2$ (Ans $\to$ D)