**High School Number Sense Lesson 59: Adding a Fibonacci Sequence**

We have had 5 lessons on sequences so far. In two of the lessons, we identified a specific term in the sequence (

**SeqNextTerm**and

**SeqNthTerm**). In the other three lessons, we added all the numbers in the sequence (

**AddSequence**,

**AddSeqOdd**, and

**AddSeqEven**). Today we will introduce the

**Fibonacci sequence**. This concept appeared

**7 times**last year, with a median placement at

**question # 57**.

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In the

**Fibonacci sequence**, each number (after the first two) is the sum of the two preceding terms. The first 15 terms of the original Fibonacci sequence are:

**1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610**

On number sense tests, you will be asked to add a series of numbers that follow the Fibonacci pattern. They may or may not be the exact same numbers in the original Fibonacci sequence; they could be any numbers that follow the same rules. For example,

**2 + 4 + 6 + 10 + 16 + 26 + 42**would fit into this category.

**How to Solve (think "2+2-2"):**

**Double**the last term.- Add the
*penultimate*(**2nd**-to-last) term. - Subtract the
**2nd**term.

**Example 1: 2 + 4 + 6 + 10 + 16 + 26 + 42 = ___**

- Double the last term: 2 x 42 =
**84**. - Add the 2nd-to-last term: 84 + 26 =
**110**. - Subtract the 2nd term. 110 - 4 =
**106**.

**Example 2: 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 = ___**

- Double the last term: 2 x 21 =
**42**. - Add the 2nd-to-last term: 42 + 13 =
**55**. - Subtract the 2nd term: 55 - 1 =
**54**.

**Example 3: 2 + 7 + 9 + 16 + 25 + 41 + 66 + 107 = ___**

- Double the last term: 2 x 107 =
**214**. - Add 66 to get
**280**. - Subtract 7 to get
**273**.

**Example 4: 5 + 9 + 14 + 23 + 37 + ... + 157 + 254 = ___**

- Double 254 to get
**508**. - Add 157 to get
**665**. - Subtract 9 to get
**656**.

Example 5: 6 + 10 + 16 + 26 + ... + 288 + 466 = ___

Example 5: 6 + 10 + 16 + 26 + ... + 288 + 466 = ___

- (This was question # 59 on last year's UIL state test). Double 466 to get
**932**. - Add 288 to get
**1220**. - Subtract 10 to get
**1210**.

**Example 6: The sum of the first 10 terms of the Fibonacci type sequence 0, 3, 3, 6, 9, 15, ... is ___**

- We have 6 terms so far. The next 4 terms are 24, 39, 63, and 102.
- Double the last term to get
**204**. - Add 63 to get
**267**. - Subtract 3 to get
**264**.

**Here's a free worksheet to help you practice AddSeqFibon:**

addseqfibon.pdf |

**Up Next for High School: BaseMult**