Find a formula for the sum of the first n terms of the sequence. $17,21,25,29,33 , \ldots$
A) $S _ { n } = n ( 2 n + 15 )$
B) $S _ { n } = n ( 5 n + 1 )$
C) $S _ { n } = \frac { ( n + 1 ) } { n }$
D) $S _ { n } = n ( 2 n + 1 )$
E) $S _ { n } = n ( 17 n - 1 )$

Question

Find a formula for the sum of the first n terms of the sequence.   $17,21,25,29,33 , \ldots$  
A) $S _ { n } = n ( 2 n + 15 )$
B) $S _ { n } = n ( 5 n + 1 )$
C) $S _ { n } = \frac { ( n + 1 ) } { n }$
D) $S _ { n } = n ( 2 n + 1 )$
E) $S _ { n } = n ( 17 n - 1 )$

Quizplus · Accepted Answer

This sequence is an arithmetic sequence with the first term $a_1 = 17$ and common difference $d = 4$. The sum of the first $n$ terms of an arithmetic sequence is given by $S_n = \frac{n}{2}[2a_1 + (n-1)d]$. Substituting $a_1 = 17$ and $d = 4$ gives $S_n = \frac{n}{2}[34 + 4(n-1)] = \frac{n}{2}[34 + 4n - 4] = \frac{n}{2}[30 + 4n] = n(15 + 2n) = n(2n + 15)$, which matches option A.

Find a Formula for the Sum of the First N 17,21,25,29,33,…17,21,25,29,33 , \ldots17,21,25,29,33,…

Find a Formula for the Sum of the First N $17,21,25,29,33 , \ldots$