Multiple choice

What is the sum of the first $n$ terms if the first term is $2$, the common difference is $5$ and the $n^{th}$ term is $122$ in an arithmetic series?

  1. $1250$
  2. $1350$
  3. $1450$
  4. $1550$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

a = 2, d = 5, Tn = 122. 122 = 2 + (n-1)5 => 120 = (n-1)5 => 24 = n-1 => n = 25. Sum = (n/2)(a + Tn) = (25/2)(2 + 122) = (25/2)(124) = 25 * 62 = 1550.

AI explanation

Use the sum formula when the first and last terms are known: Sn = n/2 * (a + l). The first term a is 2 and the last term l is 122. First, find the number of terms using the nth term formula an = a + (n-1)d, which gives 122 = 2 + (n-1)*5, meaning 120 = (n-1)*5, so n-1 = 24 and n = 25. Then, the sum is S25 = 25/2 * (2 + 122) = 25/2 * 124 = 25 * 62 = 1550.

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