Discrete Mathematics Answers

Write the formula of the following sequence, identify if explicit or recursive formula or both.

1. 1.3,5.7

2. 1, -1, 1, -1

3. 1, 4, 7, 10, 13, 16

4. 0, 3, 8, 15, 24, 25

5. 0, 2, 0, 2, 0, 2 ...

6.1, 1/2, 1/4, 1/8, 1/16

7. 0, 1, 1, 2, 3, 5, 8, 13 ... (fibonacci sequence)

Write the first 4 terms of the following formula, start with n = 1.

1. an = 5n
2. nbn = 3!bn = 3n bn = 3n^2 +2n - 6
3. gn = 1 × 2 × ... n
4. c₁ = 2.5, cn = cn_-1 + 1.5
5. d1 = -3, dn = -2d_n-1 + 1

1. Blue taxi inc. charges $7.50 for the first 4 miles and 1 dollar for each additional miles. The table shows the cost of travelling from 4 to 10 miles.

Mileage Cost

4. 7.50

5. 8.50

6. 9.50

7. 10.50

8. 11. 50

9. 12.50.

10. 13.50

• Write the recursive formula.
• Write the explicit formula

2. If the sequence formula is given as t_{n =} n² -1, n less than or equal to 1.

• Write the first five terms of the sequence
• Write the 55th term

Write the sequence of the following explicit formula:

1. sn = (-4)n , 1 <_ n

2. t_n = 92 -5n, 1<_n <_5

1. A debating team consists of three boys and two girls. Find the number n of ways they can sit in a row if the boys and girls are each to sit together.

I am having trouble with the following problem. I am unsure on how to even start.

Use propositional logic to prove that the following argument are valid:

(A⟶B) ⋀ (A⟶(B⟶C)) ⟶ (A⟶C)

solve these non-homogeneous recurrence relation an+ 4an-1 − 5an-2=n+2 where a0=1 & a1=-1

In a school, students must take at least one of these subjects: Maths, Physics or Chemistry. In a group of 50 students, 7 take all three subjects, 9 take Physics and Chemistry only, 8 take Maths and Physics only and 5 take Maths and Chemistry only. Of these 50 students, x take Maths only, x take Physics only and x + 3 take Chemistry only. Draw a Venn diagram, find X i and hence find the number taking Maths.

By using mathematical induction prove that (n+1)! > 2^(n+1) for n, where n is a positive integer greater than or equal to 4

2. For each of these sentences, determine whether an inclusive or, or an exclusive or, is intended.

Explain your answer.

a) Experience with C++ or Python is required.

b) Lunch includes soup or salad.

c) Publish or perish.

d) To enter the country you need a passport or

an ECOWAS Identity Card.

3. Determine whether each of these conditional statements is true or false.

a) If 3 + 1 = 5, then unicorns exist.

b) If 3 + 1 = 5, then dogs can fly.

c) If 4 x 4 = 16 then 3 + 5 = 8.

d) If 49 is a perfect square then 9 is prime.