The sum of three consecutive terms of an AP is 15 and
sum of their squares is 83. Find the terms
Answers
Step-by-step explanation:
(x+y)²+(x-y)² = 2(x²+y²) */
implies 2a^{2}+2d^{2}+a^{2}=83⟹2a
2
+2d
2
+a
2
=83
implies 3a^{2}+2d^{2}=83⟹3a
2
+2d
2
=83
implies 3 times 5^{2}+2d^{2}=83⟹3×5
2
+2d
2
=83
* From (1) *
implies 75+2d^{2}=83⟹75+2d
2
=83
implies 2d^{2}=83-75⟹2d
2
=83−75
implies 2d^{2}=8⟹2d
2
=8
implies d^{2}= frac {8}{2}⟹d
2
=
2
8
implies d^{2}=4⟹d
2
=4
implies d = \sqrt{4}⟹d=
4
\implies d = ±2 ---(2)⟹d=±2−−−(2)
Therefore,
a = 5 and d = ±2a=5and=±2
begin Case 1 If a=5 d=2 then Required terms are (a-d), a , (a-d) (5-2),5,(5+2)3,5,7 Case2 : If a=5 and d = -2 ,then Required terms are (5+2),5,(5-2)=7,5,
Case1:Ifa=5d=2then
Required terms are
(a−d),a,(a−d)
(5−2),5,(5+2)
3,5,7
Case2:Ifa=5andd=−2,
then
Requiredtermsare
(5+2),5,(5−2)
=7,5,3
Step-by-step explanation:
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