Question

Can you work out the pattern? You add the first two numbers together to get the third number, add the second and third numbers together to get the fourth number. You add the third and fourth numbers together to get the fifth number. You continue adding two consecutive numbers to get the next number. You are only given the first number and the last number of a cell. You must work out a method to complete the numbers in a cell if you are only given the first and last numbers of the cell.

For a 3-Cell:
A. 4, 6, 10
B. 4, 8, 12
C. 5, 7, 12
D. 3, 6, 9

For a 4-Cell:
A. 6, 10, 15, 25
B. 5, 9, 14, 23
C. 7, 12, 19, 31
D. 8, 14, 22, 35

For a 5-Cell:
A. 10, 15, 25, 40, 65
B. 8, 13, 21, 34, 55
C. 12, 18, 29, 47, 76
D. 6, 11, 19, 31, 50

Answer 1

To complete the numbers in a sequence given only the first and last number, apply arithmetic progression techniques to deduce the missing numbers using addition and solving for the unknowns in a step-by-step manner.

Step-by-step explanation:

The student is asking for help with understanding a numeric pattern where two consecutive numbers are added to generate the next number in the sequence. To work out a pattern when given only the first and last numbers of a cell, it is necessary to understand and apply the properties of sequence and series, which is a concept in Mathematics, particularly in the arithmetic progression and Fibonacci-like sequences. Let's look at each case and fill in the missing numbers.

For a 3-Cell

B. 4, 8, 12: Starting with 4, we add the next hypothetical number (x) to get the last number: 4 + x = 12. Solving for x, we get x = 8.

For a 4-Cell

C. 7, 12, 19, 31: We start with 7, add an unknown (y) to get the second number: 7 + y = 12. Then, y = 5. We continue by adding 12 to the next unknown (z) which gives us the third number: 12 + z = 19. Solving for z, we find z = 7. Finally, adding the third and fourth numbers (19 + 12) gives us the last number, 31.

For a 5-Cell

D. 6, 11, 19, 31, 50: We start with 6 and add an unknown (a) to get 11, so a = 5. Adding 11 to another unknown (b) gives us 19, so b = 8. With this pattern, we continue to the next sequence of adds to reach the last number 50.

While determining each sequence's missing numbers, the concept of commutativity (A+B = B+A) is applied, which is a fundamental property of addition in Mathematics.