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Question
Which term of the A.P. `-11/2, -3, -1/2`.... is `49/2`?
Solution
Here, a = `-11/2` and
d = `-3 - (-11/2)`
= `-3 + 11/2`
d = `5/2`
Let the given term is nth term, i.e. an = `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 13th term is `49/2`.
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