Question

an ap consists of 3terms whose sum is 15 and sum ofvthevsquares of the extremes is 58.find the terms

Answer 1

Let a-d, a, a+d are three terms in AP.

Sum of 3 terms = 15
(a-d) + (a) + (a+d) = 15
a-d+a+a+d = 15
3a-d+d = 15
3a = 15
a = 15/3
a = 5 -------(1)

Sum of the squares of the extremes = 58
(a-d)²+(a+d)² = 58
a²-2ad+d² + a²+2ad+d² = 58
a²+a²+d²+d² = 58
2(a²+d²) = 58
a²+d² = 58/2
a²+d² = 29
(5)²+d² = 29 [from eq.(1)]
25+d² = 29
d² = 29-25
d² = 4
d = √4
d = 2 OR d = -2


The required three terms are 

if a=5 , d=2           
a-d, a, a+d
(5-2),5,(5+2)
3,5,7

if a=5 , d=-2
a-d, a, a+d
[5-(-2)], 5, [5+(-2)]
7,5,3

Answer 2

Answer:

Step-by-step explanation: