Find four consecutive terms in AP whose sun is 20 and the sum of whose

1.	Find four consecutive terms in AP whose sun is 20 and the sum of whose square is 120 ?
Answer» Ans. Let first term of A.P. is a-2dCommon difference is d,Then four terms are, a-2d, a-d, a and a+dAccording 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 = 120put value of d from (1)=> (a - 4a+20)2\xa0+(a-2a+10)2\xa0+\xa0a2 +(a+2a-10)2= 120=> (20-3a)2 + (10-a) + a2 + (3a-10)2\xa0= 120=> 400 + 9a2 - 120a + 100+ a2- 20a + a2+ 9a2\xa0+ 100 - 60a = 120=> 20a2 - 200a + 600 = 120divide by 20=> a2 - 10a + 30= 6=> a2 - 10a + 24\xa0= 0=> a2\xa0- 6a - 4a + 24 =0=> a(a-6) -4(a-6) = 0=> (a-6)(a-4) = 0=> a = 6, 4if a = 6 then d = 2and if a = 4 then d = -2First A.P = 2, 4, 6, 8,....second A.P. = 8, 6, 4, 2,...\xa0\xa0

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