Q15 of 176 Page 8

Solve for x

25+22+19+ 16+...+x= 115

Here, a = 25, d = 22 – 25 = -3 and Sn = 115






⇒ 230 = n[53 – 3n]


⇒ 3n2 – 53n + 230 = 0


⇒ 3n2 – 30n - 23n + 230 = 0


⇒ 3n(n – 10) - 23(n – 10) = 0


⇒ (3n – 23)(n – 10) = 0


⇒ 3n – 23 = 0 or n – 10 = 0


⇒ or n = 10


But is not an integer.


∴ n = 10


⇒ x = a10 = a + 9d = 25 + 9 × (-3) = 25 – 27 = -2


Hence, x = -2


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