Choose the One Alternative That Best Completes the Statement or Answers

Multiple Choice

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Suppose you wish to prove the statement that follows using mathematical induction. $$4 + 9 + 14 + \ldots + ( 5 n - 1 ) = \frac { n } { 2 } ( 5 n + 3 ) , \text { for all positive integers } n$$ Let $S _ { n }$ be the statement $4 + 9 + 14 + \ldots + ( 5 n - 1 ) = \frac { n } { 2 } ( 5 n + 3 )$ . Show that $S _ { 1 }$ is true.

A) Since $4 + 9 = 13 = \frac { 2 } { 2 } ( 5 ( 2 ) + 3 ) , S _ { 1 }$ is true.
B) Since $( 5 ( 1 ) - 1 ) = 4 , S _ { 1 }$ is true.
C) Since $4 + ( 5 ( 1 ) - 1 ) = \frac { 2 } { 2 } ( 4 + 5 ( 1 ) - 1 ) , S _ { 1 }$ is true.
D) Since $\frac { 1 } { 2 } ( 5 ( 1 ) + 3 ) = \frac { 1 } { 2 } ( 8 ) = 4 , S _ { 1 }$ is true.