Use the principle of mathematical induction to find the equivalent expression for every positive integer n. $3 + 10 + 17 + \ldots + ( 7 n - 4 )$
A) $n ( 7 n - 1 )$
B) $\frac { n ( 7 n - 1 ) ^ { 2 } } { 2 }$
C) $\frac { n ( 7 n - 1 ) } { 2 }$
D) $\frac { n ^ { 2 } ( 9 n - 1 ) } { 6 }$
E) $\frac { n ( 9 n - 1 ) } { 2 }$

Question

Quizplus · Accepted Answer

The sequence is an arithmetic sequence with the first term 3 and common difference 7. The sum of the first n terms of an arithmetic sequence is given by $\frac{n}{2} \times (\text{first term} + \text{last term})$. The last term is $7n - 4$, so the sum is $\frac{n}{2} \times (3 + (7n - 4)) = \frac{n}{2} \times (7n - 1)$.

Use the Principle of Mathematical Induction to Find the Equivalent 3+10+17+…+(7n−4)3 + 10 + 17 + \ldots + ( 7 n - 4 )3+10+17+…+(7n−4)

Use the Principle of Mathematical Induction to Find the Equivalent $3 + 10 + 17 + \ldots + ( 7 n - 4 )$