Given: Let Fib (n) be the nth term of the Fibonacci Sequence, with Fib(1) = 1, Fib (2) = 1, Fib(3) = 2, and so on. Find the following.
a. Fib (8) ?		b. Fib (15)?		Fib (20)?


If Fib (20) is 790 and Fib (22) is 920. What is 	a.) Fib (21) ?		b.) Fib (19) ?


Consider Fib(3) = 2 and Fib (4) = 3, find Fib (6) , Fib (9) and Fib (12). What do you notice about third Fibonacci number?


 Given: Fib (4) = 1/8  and Fib (6) = 3/4 .   Find the following:
Fib (5)?	b.  Fib (7) ?

A sequence of terms {Un}, n ≥ 1 is defined by the recurrence relation Un + 2 = mUn, where m is a constant. Given also U1 = 2 and U2 = 5.
a. find an expression in terms of m for U3.
b. find an expression in terms of m for U4.
Given the value of U4 = 21:
c. find the possible values of m.

Let's break down each part of the problem step by step:

### Part 1: Fibonacci Sequence Calculation
We are given the standard Fibonacci sequence where:
- Fib(1) = 1
- Fib(2) = 1
- Fib(3) = 2
- Fib(4) = 3, and so on, where each term is the sum of the two preceding terms.

#### a) Fib(8):
Using the Fibonacci rule \( \text{Fib}(n) = \text{Fib}(n-1) + \text{Fib}(n-2) \):
- Fib(3) = 2
- Fib(4) = 3
- Fib(5) = 5
- Fib(6) = 8
- Fib(7) = 13
- **Fib(8) = 21**

#### b) Fib(15):
Continuing the pattern:
- Fib(9) = 34
- Fib(10) = 55
- Fib(11) = 89
- Fib(12) = 144
- Fib(13) = 233
- Fib(14) = 377
- **Fib(15) = 610**

#### c) Fib(20):
You stated that Fib(20) = 790. Hence, this is provided directly.

### Part 2: Finding Fib(21) and Fib(19) using Fib(20) = 790 and Fib(22) = 920

#### a) Fib(21):
We know from the Fibonacci property that:
\[ \text{Fib}(22) = \text{Fib}(21) + \text{Fib}(20) \]
Thus, Fib(21) can be found as:
\[ 920 = \text{Fib}(21) + 790 \]
\[ \text{Fib}(21) = 920 - 790 = 130 \]

#### b) Fib(19):
Using the same idea:
\[ \text{Fib}(20) = \text{Fib}(19) + \text{Fib}(18) \]
But we can also use the reverse property:
\[ \text{Fib}(21) = \text{Fib}(20) + \text{Fib}(19) \]
Substituting the values:
\[ 130 = 790 +

Given: Let Fib (n) be the nth term of the Fibonacci Sequence, with Fib(1) = 1, Fib (2) = 1, Fib(3) = 2, and so on. Find the following.
 a. Fib (8)? b. Fib (15)? Fib (20)?
 If Fib (20) is 790 and Fib (22) is 920. What is a.) Fib (21)? b.) Fib (19)?
 Consider Fib(3) = 2 and Fib (4) = 3, find Fib (6), Fib (9), and Fib (12). What do you notice about the third Fibonacci number?
 Given: Fib (4) = 1/8 and Fib (6) = 3/4. Find the following: Fib (5)? b. Fib (7)?
 A sequence of terms {Un}, n ≥ 1 is defined by the recurrence relation Un + 2 = mUn, where m is a constant. Given also U1 = 2 and U2 = 5.
 a. Find an expression in terms of m for U3.
 b. Find an expression in terms of m for U4.
 Given the value of U4 = 21:
 c. Find the possible values of m.

Learn how to calculate Fibonacci sequence terms like Fib(8), Fib(15), Fib(21) and solve recurrence relations. This problem involves key concepts in sequences, recurrence relations, and properties of the Fibonacci sequence, suitable for Grades 9-12.

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