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Question
Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.
Solution
Yes.
Let the first term, common difference and the number of terms of an AP are a, d and n respectively.
Let the nth term of an AP be 55
i.e., Tn = 55
We know that,
The nth term of an AP,
Tn = a + (n – 1)d ...(i)
Given that,
First term (a) = 7
and common difference (d) = 10 – 7 = 3
From equation (i),
55 = 7 + (n – 1) × 3
⇒ 55 = 7 + 3n – 3
⇒ 55 = 4 + 3n
⇒ 3n = 51
∴ n = 17
Since, n is a positive integer.
So, 55 is a term of the AP.
Since, n = 17
Therefore, 17th term of an AP is 55.
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