Q40 of 176 Page 8

In an A.P. the first term is 2, and the sum of the first five terms is one-fourth of the next five terms. Show that its 20th term is — 112.

Given: first term, a = 2


And


Sum of first five terms


Sum of next 5 terms




⇒ 4S5 = S10 – S5


⇒ 5S5 = S10




⇒ 20 + 20d = 8 + 18d


⇒ 20d – 18d = 8 – 20


⇒ 2d = -12


⇒ d = -6


Thus, a = 2 and d = -6


∴ a20 = a + (n – 1)d


⇒ a20 = 2 + (20 – 1)(-6)


⇒ a20 = 2 + (19)(-6)


⇒ a20 = 2 – 114


⇒ a20 = -112


Hence Proved


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