An A.P. consists of 57 terms of which 7th term is 13 and the last term is 138. Find the 45th term of this A.P.

Question

KnowledgeBoat · Accepted Answer

Number of terms in A.P. (n) = 57 Given, We know that, an = a + (n - 1)d ⇒ a7 = a + 6d ⇒ a + 6d = 13 ....(1) ⇒ a57 = a + 56d ⇒ a + 56d = 138 ....(2) Subtracting equation (1) from equation (2), we get: ⇒ (a + 56d) - (a + 6d) = 138 - 13 ⇒ 50d = 125 ⇒ d = ⇒ d = 2.5 Substituting value of d in equation (1), we get : ⇒ a + 6(2.5) = 13 ⇒ a + 15 = 13 ⇒ a = 13 - 15 ⇒ a = -2 45th term: ⇒ a45 = a + (45 - 1)d ⇒ a45 = -2 + (45 - 1)(2.5) ⇒ a45 = -2 + 110 ⇒ a45 = 108. Hence, the 45th term of this A.P. = 108.

Mathematics

An A.P. consists of 57 terms of which 7^th term is 13 and the last term is 138. Find the 45^th term of this A.P.

AP

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Mathematics

An A.P. consists of 57 terms of which 7th term is 13 and the last term is 138. Find the 45th term of this A.P.

AP

Related Questions

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An A.P. consists of 57 terms of which 7^th term is 13 and the last term is 138. Find the 45^th term of this A.P.

The first term of an A.P. is 20 and the sum of its first seven terms is 2100; find the 31^st term of this A.P.

Find the sum of last 8 terms of the A.P.
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The sum of the 2^nd term and the 7^th term of an A.P. is 30. If its 15^th term is 1 less than twice of its 8^th term, find the A.P.