1. If

*a*_{1}= 5 and*a*_{k+1}= 3*a*_{k}, for*k*≥ 1, then*a*_{4}= 135.2. If

*a*_{0}= 5 and*a*_{k}= 3*a*_{k}_{-1}, for*k*≥ 1, then*a*_{4}= 135.4. The fourth term of the arithmetic sequence with

*a*= 3 and*d*= 4 is 19.5. The sum of the first four terms of the arithmetic sequence with

*a*= 3 and*d*= 4 is 36.10. The Fibonacci sequence is defined by

*f*_{1}= f_{2}= 1 and, for*k*≥ 3,*f*_{k}= f_{k}_{-1 }+*f*_{k}_{-2}1a. Sequence: 1, 5, 5

^{2}, 5^{3}, 5^{4}, …1b. Sequence: 5, 3, 1, -1, -3, …

2b. Find the first seven terms of the sequence {

*a*} defined by_{n}*a*_{1}= 17, and for*k*≥ 1.12. A sequence is defined recursively by

*a*_{0}= 2,*a*_{1}= 3, and*a*= 3_{n}*a*_{n}_{-1}– 2*a*_{n}_{-2 }for*n ≥*2. a) Find the first five terms of this sequence

b) Guess a formula for

*a*._{n}15a. If five points are selected on a circle and each pair is joined with a line, into how many regions has the circle been divided?

15b. What do you think happens in general with

*n*points? Guess a formula and investigate with*n*= 6.