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SoweThe sum of first 10 terms of an Arithmetic Progression is 55 and the sum of first 9 termsof the same arithmetic progression is 45. Then its 10th term is.A) 9B)55C) 12D)10 |
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Answer» Answer: 10 (OPTION D) Step-by-step explanation: Given, S₉ = 45, S₁₀ = 55 ⇒ S₁₀ = 1st term + 2ND term + ... 10th term ⇒ S₁₀ = sum of first 9 term + 10th term ⇒ S₁₀ = S₉ + T₁₀ ⇒ 55 = 45 = T₁₀ ⇒ 10 = T₁₀ Hence the 10th term is 10 Technique 2: S₁₀ = (10/2)[2a + 9d] = 10a + 45d = 55 S₉ = (9/2)[2a + 8d] = 9a + 36d = 45 Solving these equations, we get a = 1, and d = 1 Hence 10th term = a + 9d = 1 + 9(1) = 10 |
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