A+ Answers



1. If a1 = 5 and ak+1 = 3ak, for k ≥ 1, then a4 = 135.
2. If a0 = 5 and ak = 3ak-1, for k ≥ 1, then a4 = 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 f1 = f2 = 1 and, for k ≥ 3,  fk = fk-1 fk-2
1a.       Sequence: 1, 5, 52, 53, 54, …
1b.       Sequence: 5, 3, 1, -1, -3, …
2b.       Find the first seven terms of the sequence {an} defined by a1 = 17, and for k ≥ 1.
12. A sequence is defined recursively by a0 = 2, a1 = 3, and an = 3an-1– 2an-2 for n ≥ 2.
         a) Find the first five terms of this sequence
         b) Guess a formula for an.
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.