Multiple choice

The $11^{th}$ term of the series $ \displaystyle -5,\frac{-5}{2},0,\frac{5}{2},\cdots$ is

  1. $20$
  2. $30$
  3. $40$
  4. $50$
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A Correct answer
Explanation

This is an arithmetic progression with first term a = -5 and common difference d = (-5/2) - (-5) = 2.5. The 11th term is a + 10d = -5 + 10(2.5) = -5 + 25 = 20.

AI explanation

We identify the given sequence as an arithmetic progression where the first term a is -5 and the common difference d is 5/2. Using the formula for the nth term of an arithmetic progression, Tn = a + (n - 1)d, we substitute the known values to get T11 = -5 + (11 - 1)(5/2). This simplifies to -5 + 10(5/2), which equals -5 + 25, giving a result of 20. The result is 20.

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