4.3.2 Adding Consecutive Terms of Arbitrary Fibonacci Sequence, Method 2

This method uses your knowledge of the Standard Fibonacci Sequence, $F_n$, instead of computing additional terms.

The Formula

$$\text{Sum of first } n \text{ terms} = A_1 \times F_n + A_2 \times (F_{n+1} - 1)$$

Example: Sum of first 7 terms of 4, 7, 11, …, 47, 76

$$X = 4 \times F_7 + 7 \times (F_8 - 1) = 4 \times 13 + 7 \times (21 - 1) = 52 + 140 = 192$$

Standard Fibonacci Reference

n	F_n
1	1
2	1
3	2
4	3
5	5
6	8
7	13
8	21
9	34
10	55
11	89
12	144

Tip: This method requires memorizing Standard Fibonacci Numbers but avoids computing sequence terms!

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Problem Set 4.3.2

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