In an arithmetic sequence with 25 terms, if the first term is 60 and last term is -12, the sum of the terms of the sequence is
Explanation
To find the sum of the terms in an arithmetic sequence, use the formula for the sum of an arithmetic sequence:
\[
S_n = \frac{n}{2} \times (a_1 + a_n)
\]
where:
- \( n \) is the number of terms,
- \( a_1 \) is the first term,
- \( a_n \) is the last term,
- \( S_n \) is the sum of the terms.
Given:
- \( n = 25 \),
- \( a_1 = 60 \),
- \( a_{25} = -12 \).
Step-by-Step Calculation:
1. Substitute the values into the sum formula:
\[
S_{25} = \frac{25}{2} \times (60 + (-12))
\]
2. Calculate inside the parentheses:
\[
60 + (-12) = 48
\]
3. Substitute and simplify:
\[
S_{25} = \frac{25}{2} \times 48
\]
\[
S_{25} = 25 \times 24 = 600
\]
The sum of the terms of the sequence is 600.
The correct answer is A. 600.