Question

Sum of first four integers in ap is 20 and sum of the squares of the numbers is 120. Find the numbers

Answer 1

Answer:2,4,6,8

Step-by-step explanation:

let the integers be a,a+d,a+2d,a+3d.

Sum of the integer =20

4a+6d=20

2a+3d=10

Sum of the squares = 120

squaring and adding

4a^2+14d^2+12ad=120

rewriting

(2a+3d)^2+5d^2=120

100+5d^2=120

5d^2=20

d^2=4

d=2

From 2a + 3d=10

2a+6=10

2a=4

a=2

The required Integers are:

2,4,6,8