Question

If the sum first 10 term of an ap is 4 times the sum of its first five terms, the ratio of the first term to the common difference is

Answer 1

You just have to make equations solve them and equate them until you get in terms of 'a' and 'd'.

Answer 2

Answer: the ratio of the first term to the common difference is 2 : 1

Step-by-step explanation:

let that A.P. first term is a and common difference is d.

we know that

sum of n terms of A.P. =

$=\frac{n}{2}[2a+(n-1)*d$

so acc. to question

$\frac{10}{2}[2a+(10-1)*d=4*\frac{5}{2}[2a+(5-1)*d\\\\2a+9d=4a+8d\\\\2a=d\\\\\frac{a}{d}=\frac{1}{2}\\\\a : d=1 : 2$

so the ratio of the first term to the common difference is 2 : 1