If the sum of the first ten terms of an `A.P` is four times the sum of its first five terms, the ratio of the first term to the common difference is:

Options

A. `(1)/(2)`
B. 2
C. `(1)/(4)`
D. 4

Answer

A

Explanation

According to the question, for AP
`S_(10)=4S_(5)`
`(10)/(2)(2a+9d)=4*(5)/(2)(2a+4d)[" by " S_(n)=(n)/(2)[2a+(n-1)d]]`
`10a+45d=20a+40d`
`implies 10a=5d " " implies (a)/(d)=(1)/(2)`