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KCET2023MathematicsSequences and Series

n th term of the series 1+ 3 7 + 5 7^2 + 1 7^2 + is

Options

  1. A2 n+1 7^n
  2. B2 n-1 7^n
  3. C2 n+1 7^n-1
  4. D2 n-1 7^n-1

Correct answer

D. 2 n-1 7^n-1

Step-by-step solution

We have, aligned & 1+ 3 7 + 5 72 + 7 73 + & 1 70 + 3 7 + 5 72 + 7 73 + aligned Numerator are in AP So, T_n of AP =1+(n-1)^2=2 n-1 Denominator are in GP So, T_n of GP =7^ n-1 T_n of given series = 2 n-1 7^ n-1

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