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In an arithmetic progression, the sum of its first 5 terms is one-third of the sum of its next 5 terms. If the sum of the first 15 terms of the progression is 900 , then its 20^ th term is equal to

Options

  1. A132
  2. B1600
  3. C116
  4. D156

Correct answer

D. 156

Step-by-step solution

Let a be the first term and d be the common difference of the A.P. Given that the sum of the first 5 terms is one-third of the sum of the next 5 terms: S₅ = 1 3 (S₁₀ - S₅) 3S₅ = S₁₀ - S₅ 4S₅ = S₁₀ Using the sum formula S_n = n 2 [2a + (n-1)d] : 4 5 2 [2a + 4d] = 10 2 [2a + 9d] 10[2a + 4d] = 5[2a + 9d] 2(2a + 4d) = 2a + 9d 4a + 8d = 2a + 9d d = 2a It is also given that S₁₅ = 900 : 15 2 [2a + 14d] = 900 2a + 14d = 120 Substituting d = 2a into the equation: 2a + 14(2a) = 120 30a = 120 a = 4 Thus, d = 2(4) = 8 . The 20

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