Multiple choice

In the arithmetic series, find the sum of the first $n$ terms if the first term is $-11$, the common difference is $4$ and the $n^{th}$ term is $137.$

  1. $1394$
  2. $2394$
  3. $3394$
  4. $4394$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

a = -11, d = 4, an = 137. 137 = -11 + (n-1)4 => 148 = (n-1)4 => 37 = n-1 => n = 38. Sum = (n/2)(a + an) = (38/2)(-11 + 137) = 19 * 126 = 2394.

AI explanation

First, determine the number of terms using the nth term formula an = a + (n-1)d. With the first term a = -11, common difference d = 4, and nth term an = 137, we get 137 = -11 + (n-1)*4, meaning 148 = (n-1)*4, so n-1 = 37 and n = 38. The sum is then found using Sn = n/2 * (a + l), giving S38 = 38/2 * (-11 + 137) = 19 * 126 = 2394.

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