Choose the One Alternative That Best Completes the Statement or Answers

question 175

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.