Question

Which term of the A.P. `-11/2, -3, -1/2`.... is `49/2`?

Answer 1

Here, a = `-11/2` and

d = `-3 - (-11/2)`

= `-3 + 11/2`

d = `5/2`

Let the given term is n^th term, i.e. a_n = `49/2`

⇒ a + (n – 1)d = `49/2`

⇒ `-11/2 + (n - 1)5/2 = 49/2`

⇒ `(n - 1)5/2 = 49/2 + 11/2`

⇒ `(n - 1)5/2 = 60/2`

⇒ `(n - 1)5/2` = 30

⇒ n – 1 = `30 xx 2/5`

⇒ n – 1 = 6 × 2

⇒ n – 1 = 12

⇒ n = 12 + 1

⇒ n = 13

Thus, the 13^th term is `49/2`.