Multiple choice

Sum of the series $11+23+45+87 ...$ up to $n$ terms

  1. $10(2^n-1)+n^2$
  2. $10(2^n+1)+n^2$
  3. $20(2^n-n)+n^2$

  4. None of these
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A Correct answer
AI explanation

The difference between the terms is 12, 22, and 42, which follows the pattern 10 times 2^1 plus 2, 10 times 2^2 plus 2, and so on. The general difference between consecutive terms is 10 times 2^n plus 2, making the nth term equal to the sum of these differences plus the initial term of 11. This yields the nth term formula 10 times (2^n minus 1) plus n^2, which matches the required sum of the series up to n terms.

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