Arithmetic pricing model

Problem Statement

An installer charges $400 for the first window and $100 for each additional window.

Write the total cost for 1, 2, 3, and 4 windows.
Find a formula for the total cost $A_n$ for $n$ windows.
Find $A_{15}$ .
If the budget is strictly less than $10,000, what is the maximum number of windows?

Hints

Model $A_n$ as an arithmetic sequence with first term $400$ and difference $100$ .

Solutions

A_n=400+(n-1)100=100n+300.

So $A_{15}=1800$ . For the budget:

100n+300<10000 \implies n<97,

hence the maximum integer is $n=96$ .

Further Readings

HSC Sequences: https://vumaths.com/booklets/hsc-sequences/
HSC Vectors: https://vumaths.com/booklets/hsc-vectors/
HSC Differential Equations: https://vumaths.com/booklets/hsc-differential-equations/
HSC Probability: https://vumaths.com/booklets/hsc-probability/

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