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What is the sum of the first 11 terms of an arithmetic progression if the 4th term is 11 and the 7th term is -4?1). -752). 553). 114). 100 |
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Answer» If the first term and the common DIFFERENCE of an arithmetic progression are ‘a’ and ‘d’ respectively, then, nth term of AP = a + (n - 1)d Now, 4th term = a + 3d = 11----(1) 7th term = a + 6d = -4----(2) Subtracting (1) from (2), ⇒ 6d - 3d = -4 - 11 ⇒ 3d = -15 ⇒ d = -15/3 = -5 Substituting in (1), ⇒ a = 11 - 3(-5) = 11 + 15 = 26 ? Sum of n terms of AP = n/2 [2A + (n - 1)d] ∴ Sum of 11 terms = (11/2) × [2(26) + (11 - 1)(-5)] = (11/2) × (52 - 50) = 11/2 × 2 = 11 |
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