Question

The sum of first ten terms of a AP is four times the sum of its first five terms. Then ratio of first term and common difference is

• A. $2$
• B. $\frac{1}{2}$
• C. $4$
• D. $\frac{1}{4}$

Answer 1

The correct option is B $\frac{1}{2}$

let the first term $=a$

common difference $=d$

$S_{10}=\frac{10}{2}[2a+(10-1\left)d\right]=S(2a+9d)$

and $S_5=\frac{5}{2}[2a+(5-1\left)d\right]=\frac{5}{2}(2a+4d)$

as per question,

$S_{10}=4\left(S_5\right)$

$5(2a+9d)=4\left[\frac{5}{2}\right(2a+4d\left)\right]$

$2a+9d=2(2a+4d)$

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

$\therefore d=2a$

or $\frac{a}{d}=\frac{1}{2}$