Recurrence Relations : Lines and Planes; Savings and Interest; n-Digit Ternary Sequences

1) Find and solve a recurrence relation for the number of n-digit ternary sequences with no consecutive digits being equal.

2) Find and solve a recurrence relation for the number of infinite regions formed by n infinite lines drawn in the plane so that each pair of lines intersects at a different point.

3) Find and solve a recurrence relation for the number of different regions formed when n mutually intersecting planes are drawn in three-dimensional space such that no four planes intersect at a common point and no two planes have parallel intersection lines in a third plane. (Hint: reduce to a two-dimensional problem.)

4) Suppose a savings account earns 5 percent a year. Initially there is $1000 in the account, and in year k, $10k are withdrawn. How much money is in the account at the end of n years if:
A) Annual withdrawal is at year's end?
B) Withdrawal is at start of year?

5) Find and solve a recurrence relation for the number of n-digit ternary sequences in which no 1 appears to the right of any 2.

Recurrence Relations and Lines and Planes; Savings and Interest; n-Digit Ternary Sequences are investigated. The solution is detailed and well presented.

Please help with the following discrete math involving recurrencerelations, compound interest, polynomials, number of combinations and iteration.
14. Individual membership fees at the evergreen tennis club were $50 in 1970 and have increased by $2 per year since then. Write a recurrence relation and initial conditions for

6. A string that contains only 0s 1s and 2s is called a ternary string
a) find a recurrence relation for the number of ternary strings that contain two consecutive 0s
b) what are the initial conditions
c) how many ternary strings of length six contain two consecutive 0s
The next 3 problems deal with a variation of the

Suppose a sequence satisfies the given recurrence relation and initial conditions. Find an explicit formula for the sequence
s(subk)=-4s(subk-1)-4S(subk-2), for all integers k>or equal to 2
s(sub0)=0,S(sub1)=-1

1. If a person invests in a tax-sheltered annuity, the money invested, as well as the interest earned, is not subject to taxation until withdrawn from the account. Assume that a person invests $2000 each year in a tax-sheltered annuity at 10 percent interest compounded annually. Let An represent the amount at the end of n year

See the attached file.
1. Let f be any function from R to R. Define a relation Rf by the rule: x Rf y if and only if f(x) = f(y). Show that Rf is an equivalence relation. (Hint 1: first consider a simple specific case, such as f(x) = x2. That is, x and y are related if and only if x2 = y2. Then consider the general case. H

1. Pauline takes a loan of S dollars at an interest rate of r percent per month, compounded monthly. She plans to repay the loan in T equal monthly installments of P dollars each.
a) Let a(subscript n) denote the amount Pauline owes on the loan after n months. Write a recurrence relation for a (subscript n).
b) Solve the rec

1. What is the probability that out of 3 people, 2 were born in the same month.
2. What is the probability that a seven digit phone number has 1 or more repeats.
3. What is the probability that given 5 letters selected randomly from the alphabet, none is repeated?
4. What is the probability 2 of more randomly selected s

1) Consider the sequence given by: U1 = 3.9, un+1 = un - 1.7 (n = 1,2,3,...).
i) What type of sequence is this?
ii) Please write the first four terms of the sequence.
iii) Find a closed form for the sequence.
iv) Use the closed form from 1. iii to find the value of n when un = -76
2) Consider the following geometric s