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You have two problems below. You should write psuedocode and code for each solution. Test cases are included to ensure proper functionality. You can run npm test in the terminal to run the test suite.

The Fibonacci sequence appears in nature all around us, in the arrangement of seeds in a sunflower and the spiral of a nautilus for example.

The Fibonacci sequence begins with fibonacci(0) = 0 and fibonacci(1) = 1 as its first and second terms. After these first two elements, each subsequent element is equal to the sum of the previous two elements.

Programmatically:

• fibonacci(0) = 0
• fibonacci(1) = 1
• fibonacci(n) = fibonacci(n-1) + fibonacci(n-2)

Given n, return the nth number in the sequence.

Input: 6

Output: 8

Explanation: The first 6 numbers (starting at index 0) in the fibonacci sequence are [0, 1, 1, 2, 3, 5, 8] so the 6th number is 8.

The Kaleb sequence appears nowhere in nature and exists purely in this question.

The Kaleb sequence begins with kaleb(0) = 2 and kaleb(1) = -1 as its first and second terms. After these first two elements, each subsequent element is equal to twice the previous previous term minus the previous term.

Programmatically:

• kaleb(0) = 2
• kaleb(1) = -1
• kaleb(n) = 2*kaleb(n-2) - kaleb(n-1)

Given n, return the nth number in the sequence.

Input: 6

Output: 65

TODO

Explanation: The first 6 numbers (starting at index 0) in the kaleb sequence are [2, -1, 5, -7, 17, -31, 65] so the 6th number is 65.

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