Find four consecutive terms in AP …
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Naveen Sharma 7 years, 1 month ago
Ans. Let first term of A.P. is a-2d
Common difference is d,
Then four terms are, a-2d, a-d, a and a+d
According To Ques,
=> a - 2d + a - d + a + a + d = 20
=> 4a - 2d = 20
=> 2a - d = 10
=> d = 2a - 10 ……………(1)
Also,
=> (a-2d)2 + (a-d)2 + a2 +(a+d)2 = 120
put value of d from (1)
=> (a - 4a+20)2 +(a-2a+10)2 + a2 +(a+2a-10)2= 120
=> (20-3a)2 + (10-a) + a2 + (3a-10)2 = 120
=> 400 + 9a2 - 120a + 100+ a2- 20a + a2+ 9a2 + 100 - 60a = 120
=> 20a2 - 200a + 600 = 120
divide by 20
=> a2 - 10a + 30= 6
=> a2 - 10a + 24 = 0
=> a2 - 6a - 4a + 24 =0
=> a(a-6) -4(a-6) = 0
=> (a-6)(a-4) = 0
=> a = 6, 4
if a = 6 then d = 2
and if a = 4 then d = -2
First A.P = 2, 4, 6, 8,....
second A.P. = 8, 6, 4, 2,...
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