Question

Find S12
for the arithmetic sequence 6,8,10,12,14,16,….

Answer 1

To find \( S_{12} \), which is the sum of the first 12 terms of the arithmetic sequence given, we can use the formula for the sum of the first \( n \) terms of an arithmetic sequence:

\[
S_n = \frac{n}{2} (a + l)
\]

where:
- \( n \) is the number of terms,
- \( a \) is the first term,
- \( l \) is the last term.

In this sequence:
- The first term \( a = 6 \).
- The common difference \( d = 8 - 6 = 2 \).

To find the 12th term \( l \), we use the formula for the \( n \)-th term of an arithmetic sequence:

\[
l = a + (n-1) \cdot d
\]

Substituting \( n = 12 \):

\[
l = 6 + (12-1) \cdot 2 = 6 + 11 \cdot 2 = 6 + 22 = 28
\]

Now that we have \( a \), \( l \), and \( n \), we can substitute these values into the sum formula:

\[
S_{12} = \frac{12}{2} (6 + 28) = 6 \cdot 34 = 204
\]

Thus, the sum of the first 12 terms of the arithmetic sequence is:

\[
\boxed{204}
\]