The sum of the first 5 terms of an arithmetic progression, where the common difference is non-zero, is 105. It is further given that the first, third and fourth terms of the arithmetic progression are the first 3 terms of a geometric progression. Show that the common difference of the arithmetic progression is \(-\frac{21}{2}\).[3]
Deduce that the geometric progression is convergent.[2]
Let&nbsp;\(S\) be the sum to infinity of the geometric progression, and \(A_n\) be the sum to \(n\) terms of the arithmetic progression. Find the least value of \(n\) such that the sum of \(7S\) and \(A_n\) is not positive.[4]

The sum of the first 5 terms of an arithmetic progression, where the common difference is non-zero, is 105. It is further given that the first, third and fourth terms of the arithmetic progression are the first 3 terms of a geometric progression. Show that the common difference of the arithmetic progression is \(-\frac{21}{2}\).

Deduce that the geometric progression is convergent.

Let \(S\) be the sum to infinity of the geometric progression, and \(A_n\) be the sum to \(n\) terms of the arithmetic progression. Find the least value of \(n\) such that the sum of \(7S\) and \(A_n\) is not positive.

VJC P1 Q13

VJC P1 Q13