An Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.

Here you have to find the numbers of AP with the help of their given sum and their product.

This is the Question Number 4 Exercise 11 B of RS Aggarwal Solution.

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# The sum of three numbers in AP is 3 and their product is -35. Find the numbers.

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Let a – d, a, a + d are three numbers in AP.

their sum = a – d + a + a + d = 3

3a = 3

or a = 1

Again,

Their Product = (a – d) x a x (a + d) = -35

a(a² – d²) = -35

(1² – d²) = -35

or d = ±6

d = 6 or d = -6

We have 2 conditions here:

At a = 1, d = 6

Numbers are: -5, 1 and 7

At a = 1 and d = -6

Numbers are : 7, 1, -5