Question

If the sum of the $10$ terms of an A.P. is $4$ times to the sum of its $5$ terms, then the ratio of first term and common difference is

• A. $1:2$
• B. $2:1$
• C. $2:3$
• D. $3:2$

Answer 1

Answer: (A)

$1:2$

From given, we have,

$S_{10}=4S_5$

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

$5[2a+9d]=10[2a+4d]$

$2a+9d=4a+18d$

$d=2a$

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