Equivalent Expressions and Number Sequences
Primary 6 · Mathematics
Equivalent Expressions and Number Sequences
Lesson 4 of 5
15 min
Let's begin
Uwase is training for the school race. She runs 14 km on Monday, 12 km on Tuesday, 34 km on Wednesday and 1 km on Thursday. How far will she run on Friday if she keeps the pattern? Sequences do not only use whole numbers.
0.2, 0.5, 0.8, 1.1, … Each term is 0.3 more than the one before, so the next term is 1.1 + 0.3 = 1.4.
2.5, 2.25, 2.0, 1.75, … Each term is 0.25 less, so the next term is 1.75 − 0.25 = 1.5.
Give all the fractions the same denominator, and the pattern appears.
Uwase: 14, 12, 34, 1 is the same as 14, 24, 34, 44. The numerator goes up by 1 each time, so the next term is 54 = 1 14 km.
Worked example
16, 13, 12, 23, … becomes 16, 26, 36, 46, … so the next term is 56.
Worked example
(missing middle term). 23, __, 1 13, 1 23. Write everything in thirds: 23, __, 43, 53. The gap is 13, so the missing term is 33 = 1.
12, 14, 18, 116, … Each term is half of the one before, so the next term is 132. Notice that this sequence does not have a common difference (the gaps are 14, 18, 116, which keep changing). It has a common multiplier of 12.
13, 16, 112, 124, … Again each term is half of the one before.
0.3, 0.6, 1.2, 2.4, … Each term doubles, so the next term is 4.8.
1, 12, 13, 14, … Compare it with the counting numbers 1, 2, 3, 4: they are the denominators. So the next term is 15.
Tip
With fractions, make the denominators the same first. Then the pattern in the numerators jumps out at you.
Answers
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Quick check
What is the next term? 0.3, 0.7, 1.1, 1.5, …
