Question

If four numbers are in AP such that their sum is $50$, and the greatest number is four times the least, then what is the largest the number?

Answer 1

Given, sum of $4$ terms is $50$

Thus $\text{sum}=\frac{4}{2}(2a+3d)=50$

$\Rightarrow 50=4a+6d$ .....(1)

Largest number $=a+3d$

and least number $=a$

Therefore, $a+3d=4a$

$\Rightarrow a=d$

Substituting this value in equation (1), we get

$50=4a+6a$

$\Rightarrow 10a=50$

$\Rightarrow a=5$

Thus $d=5$

Numbers are $5,10,15,20$.
Largest number$=20$