Problem [1]. Let T

To find a formula for T

n 1 2 3 4 5 6 7 8 9 FDo you see a pattern that allows you to give a formula for T_{n}1 1 2 3 5 8 13 21 34 T_{n}1 2 6 15 40 104 etc

Problem [2]. Here is a table of the even numbers:

n 1 2 3 4 5 6 7 8 ... n Evens 2 4 6 8 10 12 14 16 ... 2nNotice that the n-th even number is 2n. Now here is a table of the odd numbers:

n 1 2 3 4 5 6 7 8 ... n Odds 1 3 5 7 9 11 13 15 ... ?(a) What can we put in for "?"? I.e., give a formula in terms of n for the n-th odd number.

(b) Now let O

n 1 2 3 4 5 6 7 8 ... n Odds 1 3 5 7 9 11 13 15 ... ? OFill in more of the table. Do you see a pattern? What formula does the pattern suggest the formula for O_{n}1 4 ? ? ? ? ? ? ... ?