Question

Sum of three consecutive number of an AP is 15 and the sum of the square is 83 find the three terms

Answer 1

let the three consecutive number are a-d , a , a+d

ATQ ,

a-d+a+a+d = 15

3a = 15

a = 5 -----(1)

now , sum of the squares ,

(a-d)² +a² +(a+d)² = 83

a² + d² -2ad +a² +a² +d² +2ad = 83

3a² +2d² =83

3 ×25 + 2d² =83 ( from (1) )

75 +2d² = 83

2d² = 8

d² = 4

d = 2

so three consecutive term are

3 , 5 and 7