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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 20th term is –112.

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Answer: We have

First term = 2

Let d be the common difference of the A.P.

Therefore, the A.P. is 2, 2 + d, 2 + 2d, 2 + 3d, …

Sum of first five terms = 10 + 10d

Sum of next five terms = 10 + 35d

According to the given condition,

=>10+10d = 1/4(10+35d)

=>40+40d = 10+35d

=>30 = −5d

=>d = −6

∴ a20 = a+(20−1)d = 2+(19)(−6) = 2−114 = −112

Hence, the 20th term of the A.P. is –112.

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