Multiple choice

What is the 23rd term of the sequence 0.5, 2.0, 4.5, 8.0, ...?

  1. 264.5

  2. 278.5

  3. 300.5

  4. None of these
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A Correct answer
Explanation

The sequence is 0.5, 2.0, 4.5, 8.0. Differences: 1.5, 2.5, 3.5. This is an arithmetic progression of differences. The n-th term is a + sum of (1.5 + (k-1)*1) for k=1 to n-1. a_n = 0.5 + (n-1)/2 * (3 + (n-2)) = 0.5 + (n-1)(n+1)/2 = 0.5 + (n^2-1)/2 = n^2/2. For n=23, a_23 = 23^2 / 2 = 529 / 2 = 264.5.

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