Mathematics
Grade 9
15 min
Number sequences: word problems
Number sequences: word problems
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate a word problem into a number sequence.
Identify whether a word problem describes an arithmetic or geometric sequence.
Determine the first term (a_1), common difference (d), or common ratio (r) from a problem's context.
Apply the correct formula to find a specific term (a_n) in a real-world scenario.
Use summation formulas to calculate the total value over a period (S_n).
Solve for the number of terms (n) when given a final value.
Interpret the solution in the context of the original word problem.
Ever wonder how long it would take to save for a new phone if you save a little more each week? 📱 Let's use math to find out!
This tutorial bridges the gap between abstract sequence formulas and practical, real-world situations. You will l...
2
Key Concepts & Vocabulary
TermDefinitionExample
Number SequenceAn ordered list of numbers, called terms, that follow a specific rule or pattern.The sequence 3, 6, 9, 12, ... follows the rule 'add 3 to the previous term'.
Arithmetic SequenceA sequence where the difference between consecutive terms is constant. This represents linear growth or decay.A person saves $10 the first week, $15 the second, $20 the third. The sequence is 10, 15, 20, ... with a constant difference of $5.
Geometric SequenceA sequence where the ratio between consecutive terms is constant. This represents exponential growth or decay.A social media post gets 100 views in the first hour, 200 in the second, 400 in the third. The sequence is 100, 200, 400, ... with a constant ratio of 2.
Common Difference (d)The fixed amount added to each...
3
Core Formulas
Arithmetic Sequence Formula (nth term)
a_n = a_1 + (n-1)d
Use this to find the value of a specific term ('n') in an arithmetic sequence. 'a_1' is the first term and 'd' is the common difference.
Geometric Sequence Formula (nth term)
a_n = a_1 * r^(n-1)
Use this to find the value of a specific term ('n') in a geometric sequence. 'a_1' is the first term and 'r' is the common ratio.
Sum of a Finite Arithmetic Series
S_n = n/2 * (a_1 + a_n)
Use this to find the total sum of the first 'n' terms in an arithmetic sequence. This is useful for problems asking for a 'total amount'.
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Easy
A new coffee shop sells 120 cups on its first day. The owner projects that sales will increase by 15 cups each day. Which type of sequence does this daily sales projection represent?
A.Geometric, because the sales are multiplied by a fixed ratio.
B.Arithmetic, because a fixed number of cups is added each day.
C.Neither, because sales are unpredictable.
D.Both, because it involves numbers and a pattern.
Easy
A social media post is shared once, and then every person who sees it shares it with 3 new people. This pattern continues. Which type of sequence models the number of new shares in each round?
A.Geometric, because the number of shares is multiplied by 3 in each round.
B.Arithmetic, because the number of shares increases by a fixed amount.
C.Neither, because the growth is too rapid.
D.Arithmetic, because the number of people is added together.
Easy
A runner decides to train for a marathon. On the first day of training, she runs 3 km. Her plan is to increase her distance by 1.5 km each day. In the context of a number sequence, what is the value of the first term (a_1)?
A.1.5 km
B.4.5 km
C.3 km
D.1 km
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free