Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60, … is 300? Hence find the sum of all the terms of the Arithmetic Progression (A.P.).
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Question

Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60, … is 300? Hence find the sum of all the terms of the Arithmetic Progression (A.P.).

KnowledgeBoat · Accepted Answer

The given A.P. is 15, 30, 45, 60,...... a = 15 d = 30 - 15 = 15 an = 300 We know that, ∴ an = a + (n - 1)d ⇒ 300 = 15 + (n - 1)15 ⇒ 300 - 15 = (n - 1) 15 ⇒ 285 = (n - 1)15 ⇒ = n - 1 ⇒ 19 = n - 1 ⇒ n = 19 + 1 ⇒ n = 20 We know that, Sum of n terms of an A.P. is given by, ∴ Sn = (a + l) Now we have, a = 15 n = 20 l = 300 ⇒ S20 = (15 + 300) = 10 (315) = 3150 Hence, S20 = 3150.

Mathematics

Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60, … is 300? Hence find the sum of all the terms of the Arithmetic Progression (A.P.).

AP

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Mathematics

Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60, … is 300? Hence find the sum of all the terms of the Arithmetic Progression (A.P.).

AP

Related Questions

If the 6th term of an A.P is equal to four times its first term, and the sum of first six terms is 75, find the first term and the common difference.

The 5th term and the 9th term of an Arithmetic Progression are 4 and −12 respectively. Find:(i) the first term(ii) common difference(iii) sum of first 16 terms of the AP.

A sum of ₹ 2,800 is to be used to award four prizes. If each prize after the first is ₹ 200 less than the preceding prize, find the value of each of these prizes.

The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6th year, and 11300 in 9th year. Find the production in:(i) first year(ii) 8th year(iii) total production in 6 years.

The 5th term and the 9th term of an Arithmetic Progression are 4 and −12 respectively. Find:
(i) the first term
(ii) common difference
(iii) sum of first 16 terms of the AP.

The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6th year, and 11300 in 9th year. Find the production in:
(i) first year
(ii) 8th year
(iii) total production in 6 years.