Question

If the seventh term of anA.P. is 1/9 and ninth term is 1/7 , find its 63rd term.

Answer 1

Let a be the first term and d be the common difference of the given A.P.

Given;

a7 = 1/9 and   a9 = 1/7
a7 = a +(7 - 1) d   

[an = a + (n - 1)d]
a7 = a + 6d
1/9 = a +6d ………………(1)
a9 = a +(9- 1) d

[an = a + (n - 1)d]
a9 = a + 8d
1/7 = a+ 8d……………….(2)

Subtracting equation 2 from equation 1,
1/9 - 1/7 = a- a +6d -8d
(7 - 9)/63 = - 2d
-2 = -2d × 63
d = -2 /(-2×63)
d = 1/ 63
d =  1/ 63

Put the value of d in eq 1
1/9 = a + 6d
1/9 = a + 6 × (1/ 63)
1/9 = a + 6/63
1/9 - 6/63  =a
(7 -6 )/ 63 = a
1 /63 = a
a63 = a +62d
a63 = 1/63  + 62 × (1/63)
a63 = 1/63 +62/63
a63 = (1+62)/63
a63 = 63 / 63

a63 = 1

Hence, the value of 63rd term is 1.

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