Question

If seventh term of AP is 1/9 and it 's ninth term is 1/7 find its 63rd term

Answer 1

T7 = 1/9
a+6d = 1/9
a = (1/9)-6d -------------(1)

T9 = 1/7
a+8d = 1/7
a = (1/7)-8d --------------(2)

(1/9)-6d = (1/7)-8d
8d-6d = (1/7)-(1/9)
2d = 2/63
d = 1/63

a = (1/9)-6d
a = (1/9) - (6/63)
a = 1/63

T63
= a+62d
= (1/63) + 62×(1/63)
= (1/63)+(62/63)
= 63/63
= 1
====================
Hence the 63rd term of the given A.P is 1

Answer 2

a7 = 1/9
a + 6d = 1/9
9a + 54d = 1. ....1

a9 = 1/7
a + 8d = 1/7
7a + 56d = 1 ....2

Multiply
9a + 54d = 1 * 7
7a + 56d = 1 * 9

Subtract
(63a + 378d) - (63a + 504d) = 7-9
-126d = -2
d = 1/63

put in a + 6d = 1/9
a = 1/63

a63 = a + 62d
= 1/63 + 62/63
= 63/63
= 1

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