S_n = \frac{n}{2} \left(2a + (n - 1)d\right) = \frac{n}{2} \left(2(7) + (n - 1)(4)\right) = \frac{n}{2} (14 + 4n - 4) = \frac{n}{2} (4n + 10)

Sat, 02 May 2026 23:02:23 +0000

# S_n Formula Explained: Mastering the $n$-th Term of an Arithmetic Sequence When studying mathematics, especially algebra and sequences, one formula emerges as essential for finding the $n$-th term of an arithmetic sequence: $$
S_n = \frac{n}{2} \\left(2a + (n - 1)d\right)
$$ This elegant expression allows you to compute the sum of the first $n$ terms of any arithmetic sequence quickly — without having to add every term individually.