The first term of a sequence is 12, and each term after the first term is 2 less than the preceding term. If n is a positive integer, which of he following could be the sum of the first n terms of the sequence?

Question

The first term of a sequence is 12, and each term after the first term is 2 less than the preceding term.  If n is a positive integer, which of he following could be the sum of the first n terms of the sequence?

johnweldon1993 · Answer

Well since this would be an arithmetic sequence (subtracting 2 from the previous term) We can use the formula

$$\large a_n = a_1(n - 1)d$$

Where 'd' is the common difference (which here will be 2)

The sum of a sequence in that form will be

$$\large S_n = \frac{n(a_1 + a_n)}{2}$$

$\large a_1$ is the first term (12)
and $\large n$ is the number of terms