Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
AP
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Question

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

KnowledgeBoat · Accepted Answer

Let first term of A.P. be a and common difference be d. By formula, a_n = a + (n - 1)d Given, 2nd term = 14 ⇒ a₂ = 14 ⇒ a + (2 - 1)d = 14 ⇒ a + d = 14 ............(1) 3rd term = 18 ⇒ a₃ = 18 ⇒ a + (3 - 1)d = 18 ⇒ a + 2d = 18 ............(2) Subtracting equation (1) from (2), we get : ⇒ a + 2d - (a + d) = 18 - 14 ⇒ a - a + 2d - d = 4 ⇒ d = 4. Substituting value of d in equation (1), we get : ⇒ a + 4 = 14 ⇒ a = 10. Last term (l) = 51st term = a₅₁ = a + (51 - 1)d = 10 + 50 × 4 = 10 + 200 = 210. By formula, Sum (S) = Substituting values we get : Hence, sum of first 51 terms = 5610.

Mathematics

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

AP

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Mathematics

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

AP

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Show that a₁, a₂,……., a_n,…….. form an AP where a_n is defined as below :
(i) a_n = 3 + 4n
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Also find the sum of the first 15 terms in each case.