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Numerical

Which term of the A.P. 3, 8, 13, 18, ... is 78?

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#### Solution

3, 8, 13, 18, …

For this A.P.,

a = 3

d = a_{2} − a_{1} = 8 − 3 = 5

Let n^{th} term of this A.P. be 78.

an = a + (n − 1) d

78 = 3 + (n − 1) 5

75 = (n − 1) 5

(n − 1) = 15

n = 16

Hence, 16^{th} term of this A.P. is 78.

Concept: nth Term of an AP

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