Math  /  Discrete

Question3. What is the 50 th term of the Fibonacci Sequence?
4. What is the next term of the sequence 1,4,9,16,25,36,49,1,4,9,16,25,36,49, \ldots
5. What is the missing number in the sequence 3,5,93,5,9, \qquad 15,23,3315,23,33 ? \qquad \qquad \qquad
6. What is the next three terms of the sequence 10,9,7,4,0,10,9,7,4,0, \ldots ? \qquad \qquad \qquad
7. What is the missing number in the sequence 10,6,2-10,-6,-2, \qquad 6,10 ? \qquad \qquad
8. What is the missing number in the sequence 21 , \qquad 18,15,12,9?18,15,12,9 ? \qquad \qquad \qquad
9. Describe the nature of the number pattern 88,77,55,22,88,77,55,22, \ldots \qquad \qquad

Studdy Solution
Use the recurrence relation to compute up to F50 F_{50} :
\begin{align*} F_2 &= F_1 + F_0 = 1 + 0 = 1 \\ F_3 &= F_2 + F_1 = 1 + 1 = 2 \\ F_4 &= F_3 + F_2 = 2 + 1 = 3 \\ &\vdots \\ F_{50} &= F_{49} + F_{48} \end{align*}
This can be efficiently calculated using a loop or iterative method in programming. Here, we'll use an iterative approach:
\begin{align*} F_{50} &= 12586269025 \end{align*}
The 50th term of the Fibonacci sequence is 12586269025 12586269025 .
### 4. What is the next term of the sequence 1,4,9,16,25,36,49, 1,4,9,16,25,36,49, \ldots ?
_ASSUMPTIONS_:
1. The sequence appears to follow a pattern related to squares of integers.
2. Identify the pattern to find the next term.

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