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BECE Mathematics 2015 Paper

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Question : 39

Total: 40

Find the missing number in the sequence below:

11,16,22,29,-,46,56.

30
36
37
39

Solution:

When analyzing the sequence, you will realize the rule for the sequence is:

U_n = U_{n-1} + 3 + n

Where

n \geq 2

When

n=2

\; U_2 = U_{2-1} + 3 + 2

\; U_2 = U_1 + 5

\; U_1 = 11

\; U_2 = 11 + 5 = 16

When

n=3

\; U_3 = U_{3-1} + 3 + 3

\; U_3 = U_2 + 6

\; U_2 = 16

\; U_3 = 16 + 6 = 22

When

n=4

\; U_4 = U_{4-1} + 3 + 4

\; U_4 = U_3 + 7

\; U_3 = 22

\; U_4 = 22 + 7 = 29

When

n=5

\; U_5 = U_{5-1} + 3 + 5

\; U_5 = U_4 + 8

\; U_4 = 29

\; U_5 = 29 + 8 = 37

When

n=6

\; U_6 = U_{6-1} + 3 + 6

\; U_6 = U_5 + 9

\; U_5 = 37

\; U_6 = 37 + 9 = 46

When

n=7

\; U_7 = U_{7-1} + 3 + 7

\; U_7 = U_6 + 10

\; U_6 = 46

\; U_7 = 46 + 10 = 56

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