Use mathematical induction to solve for all positive integers n. $5 + 9 + 13 + 17 + \ldots + ( 4 n + 1 ) = ?$
A) $n ( 9 n + 3 )$
B) $\frac { n ( 2 n + 3 ) } { 2 }$
C) $n ( n + 3 )$
D) $\frac { n ( n + 3 ) } { 9 }$
E) $n ( 2 n + 3 )$

Question

Use mathematical induction to solve for all positive integers n.​ $5 + 9 + 13 + 17 + \ldots + ( 4 n + 1 ) = ?$ ​
A) $n ( 9 n + 3 )$
B) $\frac { n ( 2 n + 3 ) } { 2 }$
C) $n ( n + 3 )$
D) $\frac { n ( n + 3 ) } { 9 }$
E) $n ( 2 n + 3 )$

Quizplus · Accepted Answer

The sequence is an arithmetic sequence with the first term 5 and a common difference of 4. The sum of the first n terms of an arithmetic sequence is given by $S_n = \frac{n}{2} (2a + (n-1)d)$. Substituting $a = 5$, $d = 4$, and simplifying, we get $S_n = n(2n + 3)$.

Use Mathematical Induction to Solve for All Positive Integers N 5+9+13+17+…+(4n+1)=?5 + 9 + 13 + 17 + \ldots + ( 4 n + 1 ) = ?5+9+13+17+…+(4n+1)=?

Use Mathematical Induction to Solve for All Positive Integers N $5 + 9 + 13 + 17 + \ldots + ( 4 n + 1 ) = ?$