Question

hs: algebra 2b m (sequential) / 6:sequences and series
15 + 19 + 23 +
options:
\\(\sum_{n=1}^{7} (11 + 4n)\\)
\\(\sum_{n=1}^{7} (13 + 2n)\\)
\\(\sum_{n=1}^{7} (9 + 6n)\\)
\\(\sum_{n=1}^{7} (10 + 5n)\\)

Explanation:

Step1: Identify sequence parameters

The given series is arithmetic: first term $a_1=15$, common difference $d=4$, number of terms $n=7$.

Step2: Find general term formula

Arithmetic sequence term: $a_n = a_1 + (n-1)d$
Substitute values: $a_n = 15 + (n-1)4 = 11 + 4n$

Step3: Match to summation form

The summation for 7 terms is $\sum_{n=1}^{7}(11 + 4n)$, which matches option A.

Answer:

A. $\sum_{n=1}^{7}(11 + 4n)$