If 3 x - 1 , 3 , x - 3 are the first three terms of an arithmetic progression, then the sum of the first five terms can be

Question

If 3 x - 1 , 3 , x - 3 are the first three terms of an arithmetic progression, then the sum of the first five terms can be, 5, 10, 20, 30

MARKS App · Accepted Answer

Case-I : x 1 3 ⇒ - 3 x + 1,3 , - x + 3 are in A . P . ⇒ 6 = - 3 x + 1 - x + 3 ⇒ 4 x = - 2 ⇒ x = - 1 2 ⇒ terms are 5 2 , 3 , 7 2 , 4 , 9 2 ⇒ sum = 35 2 Case-II: 1 3 ≤ x 3 3 x - 1,3 , - x + 3 are in A.P. ⇒ 6 = 3 x - 1 - x + 3 = 2 x + 2 ⇒ x = 2 ⇒ terms are 5 , 3 , 1 , – 1 , – 3 ⇒ sum = 5 Case-III: x ≥ 3 ⇒ terms are 3 x - 1,3 , x - 3 ⇒ 6 = 3 x - 1 + x - 3 = 4 x - 4 ⇒ 4 x = 10 ⇒ x = 5 2 not possible

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