Question

In an AP of 3 terms whose sum is is 60 and sum of squares of extremes is 850 find the terms

Answer 1

Let the 3 terms of AP is a-d ,a, a+d

Sn = n/2(a + l)

SE = 3/2 ( (a-d) + (a + d))

60 = 3/2( 2a) = 3a

a = 60/3 = 20

$(a - d) {}^{2} + (a + d) {}^{2} = 850$

$a {}^{2} + d {}^{2} - 2ad + a {}^{2} + d {}^{2} + 2ad = 850$

$2a {}^{2} + 2d {}^{2} = 850$


$a {}^{2} + d {}^{2} = 850 \div 2 = 425$

Put value of a

$20 {}^{2} + d {}^{2} = 425$

$d {}^{2} = 425 - 400 = 25$

$d = 5$

a - d = 20 - 5 = 15

a = 20

a + d = 20 + 5 = 25

Hence terms are. 15 , 20 , 25.



Thanks