*Lesson #1 - Solutions*

*Part I:*a) Pattern: add 2; Next two terms: 11, 13

b) Pattern: add 3; Next two terms: 17, 20

c) Pattern: add 5; Next two terms: 34, 39

d) Pattern: add 10; Next two terms: 60, 70

**Bonus**: Pattern: add 2.5; Next two terms 15.5, 18

**Wrap-up**: Each sequence involves ADDING the same value each time.

*Part II:*a) Pattern: subtract 5; Next two terms: 5, 0

b) Pattern: subtract 4; Next two terms: 5, 1

c) Pattern: subtract -6; Next two terms: -10, -16

d) Pattern: subtract 2; Next two terms: -7, -9

**Bonus**: Pattern: subtract 1.5; Next two terms: 1.5, 0

**Wrap-up**: Each sequence involves SUBTRACTING the same value each time.

*Part III:*a) Pattern: multiply by 2; Next two terms: 64, 128

b) Pattern: multiply by 3: Next two terms: 324, 972

c) Pattern: multiply by 1/2 (also, divide by 2, but for consistency, we'll stay with multiplication); Next two terms: 2.5, 1.25

d) Pattern: multiply by 5; Next two terms: 625, 3125

**Bonus**: Pattern: multiply by 1.5; Next two terms: 50.625, 75.9375

**Wrap-up**: Each sequence involves MULTIPLYING each term by the same value each time. (Note that on Question C, dividing by 2 is the equivalent of multiplying by 1/2.)

*Part IV:**At the conclusion of these exercises, it may be a good time to introduce children to the Fibonacci Sequence, which is given at the end of the solutions. See if they can identify the sequence as similar to those given in this section.*

a) Pattern: add up any two consecutive numbers to find the next number; Next two terms: 23, 37

b) Pattern: add up any two consecutive numbers to find the next number; Next two terms: 45, 73

c) Pattern: add up any two consecutive numbers to find the next number; Next two terms: 142, 230

d) Pattern: add up any two consecutive numbers to find the next number; Next two terms: 16, 26

**Bonus**: Pattern: add up any

*three*consecutive numbers to find the next number; Next two terms: 68, 125

**Wrap-up:**Each sequence is defined by adding up previous numbers to find the next number.

*Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, ....*
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