Number sequences: word problems

Key Notes :

Definition of Number Sequences:

  • A number sequence is a list of numbers arranged in a specific order based on a rule or pattern.

Types of Number Sequences:

  • Arithmetic Sequence: Numbers increase or decrease by a constant difference (e.g., 2, 4, 6, 8…).
  • Geometric Sequence: Numbers increase or decrease by a constant factor (e.g., 3, 6, 12, 24…).
  • Special Sequences: Includes squares (1, 4, 9, 16…) or Fibonacci sequences (1, 1, 2, 3, 5…).

Understanding Word Problems:

  • Read the problem carefully to identify the pattern or rule in the sequence.
  • Look for keywords like “each time,” “difference,” “product,” “twice as much,” etc.
  • Determine whether the sequence is increasing or decreasing.

Steps to Solve Word Problems:

  • Identify the given numbers in the sequence.
  • Find the pattern or rule (addition, subtraction, multiplication, division).
  • Use the rule to find missing numbers or extend the sequence.
  • Answer the specific question asked in the problem.

Common Rules in Sequences:

  • Addition/Subtraction: Each term is obtained by adding or subtracting a fixed number.
  • Multiplication/Division: Each term is obtained by multiplying or dividing by a fixed number.
  • Alternating Patterns: A mix of operations in a sequence (e.g., +2, -1, +2, -1…).

Examples of Word Problems:

  • If the first term of a sequence is 5 and each term increases by 3, what is the 10th term?
  • A sequence starts with 2, and each term is doubled. What is the 6th term?
  • Find the missing term in the sequence: 7, 14, __, 28.

Strategies for Success:

  • Write down the sequence and the identified rule.
  • Use tables or charts for organization if needed.
  • Check your work by plugging the rule back into the sequence.

Learn with an example

1) Cindy is picking berries in the berry patch. She picks 64 berries from the first bush, 72 berries from the second bush, 80 berries from the third bush, and 88 berries from the fourth bush. If this pattern continues.

How many berries will Cindy pick from the fifth bush?

 ______berries

First, look for a pattern.

Add 8 to find the next number:

Cindy will pick 96 berries from the fifth bush.

2) Jenny is drawing stars in her notebook. She draws 3 stars on the first page, 5 stars on the second page, 8 stars on the third page, and 12 stars on the fourth page. If this pattern continues.

How many stars will Jenny draw on the fifth page?

 _________stars

First, look for a pattern. Notice how the amount increases by 1 each time.

Add 5 to find the next number:

Jenny will draw 17 stars on the fifth page.

3) The teacher gave 110 gold stickers to the first student, 122 gold stickers to the second student, 134 gold stickers to the third student, and 146 gold stickers to the fourth student. If this pattern continues.

How many gold stickers will the teacher give to the fifth student?

 _______gold stickers

First, look for a pattern.

Add 12 to find the next number:

The teacher will give 158 gold stickers to the fifth student.

Let’s practice!🖊️