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Question

If the seventh term of an A.P. is 19 and its ninth term is 17, find its (63)rd term.

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Solution

Let a be the first term and d be the common difference.

We know that, nth term = an = a + (n − 1)d

According to the question,

a7 = 19
⇒ a + (7 − 1)d = 19
⇒ a + 6d = 19 .... (1)

Also, a9 = 17
⇒ a + (9 − 1)d = 17
⇒ a + 8d = 17 ....(2)

On Subtracting (1) from (2), we get
8d − 6d = 17-19
⇒ 2d = 9-763
⇒ 2d = 263
⇒ d = 163
⇒ a = 19-663 [From (1)]
⇒ a = 7-663
⇒ a = 163

∴ a63 = a + (63 − 1)d
= 163+6263
= 6363
= 1

Thus, (63)rd term of the given A.P. is 1.

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