If the seventh term of an AP is and its ninth term is , find its 63^rd term.

Given that, a₇ = 1/9

a₉ = 1/7

To find: a₆₃

We know that nth term is given by a_n = a + (n – 1) d

Where a = first term, n = number of terms, d = common difference.

First let us consider

⇒ a₇ = a + (7 – 1) d

⇒ 1/9 = a + 6d … (1)

Now,

⇒ a₉ = a + (9 – 1) d

⇒ 1/7 = a + 8d … (2)

Subtracting (1) from (2), we get

⇒ 2/63 = 2d

⇒ d = 1/63

Substituting value of d in (1),

⇒ 1/9 = a + 6(1/63)

⇒ a = 7/63 – 6/63

⇒ a = 1/63

Now,

a₆₃ = 1/63 + (63 – 1) 1/63

⇒ a₆₃ = 1/63 + 62/63

⇒ a₆₃ = 63/63

⇒ a₆₃ = 1

Ans. The 63^rd term of AP is 1.