Multiple choice

How many terms are there in the sequence $15\cfrac{1}{2}, 13, ......-47$?

  1. $27$
  2. $26$
  3. $28$

  4. None
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is an arithmetic progression with a = 31/2, d = 13 - 15.5 = -2.5. Last term = -47. -47 = 15.5 + (n-1)(-2.5). -62.5 = (n-1)(-2.5). n-1 = 25. n = 26.

AI explanation

The given sequence is an arithmetic progression with the first term a equal to 31/2, the common difference d equal to 13 minus 31/2 which is -5/2, and the last term equal to -47. Using the formula for the nth term, T_n = a + (n-1)d, we set -47 = 31/2 + (n-1)(-5/2). Solving this equation, -125/2 = (n-1)(-5/2), which results in n-1 = 25, meaning there are 26 terms in the sequence.

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