Question

Many interesting patterns exist between the terms of the Fibonacci sequence and the Lucas sequence. Make a conjecture about the next equation that would appear in the list shown below. Then, verify it. 1+3=2\cdot2 2+4=2\cdot3 3+7=2\cdot5 5+11=2\cdot8 8+18=2\cdot13 Each expression of the next equation in the list is equal to? on both sides.

          Many interesting patterns exist between the terms of the Fibonacci sequence and the Lucas sequence. Make a conjecture about the next equation that would appear in the list shown below. Then, verify it.
1+3=2\cdot2
2+4=2\cdot3
3+7=2\cdot5
5+11=2\cdot8
8+18=2\cdot13
Each expression of the next equation in the list is equal to? on both sides.

Many interesting patterns exist between the terms of the Fibonacci sequence and the Lucas sequence. Make a conjecture about the next equation that would appear in the list shown below. Then, verify it.
1+3=2·2
2+4=2·3
3+7=2·5
5+11=2·8
8+18=2·13
Each expression of the next equation in the list is equal to? on both sides.

Added by Robert D.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Keerti J

03/05/2022

Step 1

Step 1: We can observe that the left side of each equation is the sum of two consecutive terms in the Fibonacci sequence. Show more…

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Many interesting patterns exist between the terms of the Fibonacci sequence and the Lucas sequence. Make a conjecture about the next equation that would appear in the list shown below. Then, verify it. 1 + 3 = 2^2 2 + 4 = 2^3 3 + 7 = 2 * 5 5 + 11 = 2^4 8 + 18 = 2^5 Each expression of the next equation in the list is equal on both sides.