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CA Foundation · Quantitative Aptitude · Sequence and Series

For a series, the sum of the first n terms is Sn = 2^(n+1) - 2 - n. What is the value of the 6th term, T6?

The 6th term is 63. It equals the difference of successive sums: S6 = 128 - 8 = 120 and S5 = 64 - 7 = 57, so T6 = 120 - 57 = 63. This agrees with the general term 2 to the power n minus 1.

  1. A63Correct
  2. B62
  3. C64
  4. D57

Explanation

S6 = 2^7 - 2 - 6 = 128 - 8 = 120. S5 = 2^6 - 2 - 5 = 64 - 7 = 57. T6 = S6 - S5 = 120 - 57 = 63. The value 57 is S5, wrongly taken as the term. Check: Tn = 2^n - 1 gives 63.

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