91Ó°ÊÓ

Write the first five terms of each sequence. $$a_{n}=4 n+10$$

Write out in full and verify the statements \(S_{1}, S_{2}, S_{1} S_{4}\) and \(S_{5}\) for the following. Then use mathematical induction to prove that each statement is inue for every positive integer \(n .\) See Example 1 $$1+3+5+\cdots+(2 n-1)=n^{2}$$

On a business trip, Terry took 3 pairs of pants, 4 shirts, 1 jacket, and two pairs of shoes. Determine the number of outfits that Terry can choose.

When saddling her horse, Judy can choose from 2 saddles, 3 blankets, and 2 cinches. Find the number of possible choices for saddling Judy's horse.

Write a sample space with equally likely outcomes for each experiment Two ordinary coins are tossed.?

Write the first five terms of each sequence. $$a_{n}=6 n-3$$

Write the first five terms of each sequence. $$a_{n}=\frac{n+5}{n+4}$$

Write a sample space with equally likely outcomes for each experiment Three ordinary coins are tossed.?

A conference schedule offers 2 main sessions, 20 break-out sessions, and 4 minicourses. In how many ways can an attendee choose 1 of each to attend?

Assume that \(n\) is a positive integer. Use mathematical induction to prove each statement S by following these steps. See Example \(I\). (a) Verify the statement for \(n=1\) (b) Write the statement for \(n=k\) (c) Write the statement for \(n=k+1\) (d) Assume the statement is true for \(n=k\). Use algebra to change the statement in part (b) to the statement in part (c). (e) Write a conclusion based on Steps (a)-(d). $$3+6+9+\dots+3 n=\frac{3 n(n+1)}{2}$$