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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.
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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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