# 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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