Question

When the sum of the first ten terms of an arithmetic progression is four times the sum of the first five terms, the ratio of the first term to the common differednce is

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

Answer 1

The correct option is A $1:2$

Using $S=\frac{n}{2}[2a+(n-1\left)d\right]$,

we have $\frac{10}{2}(2a+9d)$ $=4\times \frac{5}{2}(2a+4d)$

$\therefore d=2a;\therefore a:d=1:2$.