Multiple choice

In an AP, the first term and the last terms are $50$ and $-50$ respectively. The common difference is $-10$. Find the number of terms in the series

  1. $9$
  2. $10$
  3. $11$
  4. $12$
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C Correct answer
Explanation

In an AP, the n-th term is given by a_n = a + (n-1)d. Here, -50 = 50 + (n-1)(-10). Solving for n: -100 = (n-1)(-10), so 10 = n-1, which means n = 11.

AI explanation

Using the formula for the nth term of an arithmetic progression, $a_n = a + (n-1)d$, we can substitute the known values: $-50 = 50 + (n-1)(-10)$. Solving this equation yields $-100 = -10n + 10$, which simplifies to $n = 11$. The result is 11.

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