Use mathematical induction to solve for all positive integers n. $3 + 8 + 13 + 18 + \ldots + ( 5 n - 2 ) = ?$
A) $\frac { n } { 6 } ( 5 n + 1 )$
B) $n ( 5 n + 1 )$
C) $\frac { n } { 2 } ( 5 n + 1 )$
D) $\frac { n } { 4 } ( 5 n + 1 )$
E) $5 n + 1$

Question

Use mathematical induction to solve for all positive integers n.   $3 + 8 + 13 + 18 + \ldots + ( 5 n - 2 ) = ?$  
A) $\frac { n } { 6 } ( 5 n + 1 )$
B) $n ( 5 n + 1 )$
C) $\frac { n } { 2 } ( 5 n + 1 )$
D) $\frac { n } { 4 } ( 5 n + 1 )$
E) $5 n + 1$

Quizplus · Accepted Answer

The given series is an arithmetic series with the first term $a = 3$ and common difference $d = 5$. The sum of the first $n$ terms of an arithmetic series is given by $S_n = \frac{n}{2}[2a + (n-1)d]$. Substituting $a = 3$ and $d = 5$ gives $S_n = \frac{n}{2}[2(3) + (n-1)5] = \frac{n}{2}(6 + 5n - 5) = \frac{n}{2}(5n + 1)$, which matches option C.

Use Mathematical Induction to Solve for All Positive Integers N 3+8+13+18+…+(5n−2)=?3 + 8 + 13 + 18 + \ldots + ( 5 n - 2 ) = ?3+8+13+18+…+(5n−2)=?

Use Mathematical Induction to Solve for All Positive Integers N $3 + 8 + 13 + 18 + \ldots + ( 5 n - 2 ) = ?$