Question

an ap consists of 3 terms whose sum is 15 and sum of the squares of the is 83. Find the terms

Answer 1

Hi ,

Let ( a - d ) , a , ( a + d ) are in A. P

according to the problem given ,

sum of the three terms = 15

a - d + a + a + d = 15

3a = 15

a = 15 / 3

a = 5 ---( 1 )

sum of the squares of the terms = 83

( a - d )² + a² + ( a + d )² = 83

a² + 2(a² + d² ) = 83

a² + 2a² + 2d² = 83

3a² + 2d² = 83

2d² = 83 - 3a²

= 83 - 3 × 5² [ from ( 1 ) ]

= 83 - 75

2d² = 8

d² = 8/2

d² = 4

d = ± 2

Therefore ,

Required 3 terms are ,

1 ) If a = 5 , d = 2

a - d = 5 -2 = 3 ,

a = 5 ,

a + d = 5 + 2 = 7

or

2 ) If a = 5 , d = -2

a - d = 5 +2 = 7

a = 5 ,

a + d = 5 - 2 = 3

I hope this helps you.

:)