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General Term nth Term of a Sequence — Free MYP4 Mathematics (Standard) Practice Questions
1QuestionCreating a Rule for the nth TermConcept Practice
2 marks~3 minCriterion A
A gardener records the height of a bamboo plant over four consecutive days:
Day 1: 8 cm
Day 2: 11 cm
Day 3: 14 cm
Day 4: 17 cm
Day 1: 8 cm
Day 2: 11 cm
Day 3: 14 cm
Day 4: 17 cm
a
Determine the formula for , the height of the plant (in cm) after days. [1]
b
The gardener claims this linear model will reliably predict the plant's height after one year. Justify whether this claim is valid. [1]
Solutions
2QuestionFinding Term Position Given ValueAssessment Practice
7 marks~11 minCriterion D
A student opens a savings account with an initial deposit of 500 dollars. Each month, exactly 25 dollars is added, forming an arithmetic sequence.
a
Show that the account balance first reaches 875 dollars in month 16. [2]
b
The student considers making an additional one-off deposit of 200 dollars at the start of month 10. Deduce the new month in which the balance would first reach 875 dollars under this revised plan. [2]
c
The arithmetic model assumes a constant monthly increase of 25 dollars. Advise the student whether this model is reliable for predicting their long-term account balance, discussing at least two real-world factors in your response. [3]
Solutions
3QuestionDistinguishing Between Linear and Non-Linear SequencesAssessment Practice
5 marks~8 minCriterion C
A solar panel installation company charges a fixed connection fee plus a constant rate per panel installed. A technician records the following data from five recent jobs:
| Number of panels () | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Total cost in hundreds of dollars () | 3 | 7 | 11 | 15 | 19 |
a
Justify whether the relationship between and is linear or non-linear. [2]
b
Derive a formula for in terms of . [1]
c
A client has a budget of 1800 dollars. Advise the client whether this budget is sufficient for an installation of 5 panels, and explain what the -intercept represents in this context. [2]
Solutions
4QuestionEvaluating Terms Using the nth Term FormulaAssessment Practice
5 marks~8 minCriterion B
A community garden is being expanded each year. The total number of plant beds after year is modelled by and for .
a
Calculate the first four terms of the sequence, showing all working. [2]
b
Deduce a formula for the th term . [1]
c
Justify that your formula is valid for all integers , then advise the garden planners whether they should expect resource requirements to increase at a constant rate as the garden grows. [2]
Solutions
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