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QLDMath MethodsQuick questions
Unit 1: Algebra, statistics and functions
Quick questions on Arithmetic and geometric sequences (QCE Math Methods Unit 1)
8short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is loans and savings?Show answer
Compound interest gives a geometric sequence with $r = 1 + i$ where $i$ is the periodic interest rate.
What is depreciation?Show answer
Straight-line depreciation is arithmetic; declining-balance depreciation is geometric.
What is salary growth?Show answer
Fixed-dollar raise: arithmetic. Percentage raise: geometric.
What is population?Show answer
Constant absolute increase: arithmetic. Constant percentage growth: geometric.
What is confusing arithmetic and geometric?Show answer
Add or multiply? Check by computing two consecutive differences and ratios.
What is off-by-one on $n - 1$ vs $n$?Show answer
$T_n$ uses $n - 1$; $S_n$ uses $n$.
What is using sum-to-infinity when $|r| \ge 1$?Show answer
Diverges; formula does not apply.
What is mixing total and individual term?Show answer
A question asking for the year $10$ salary wants $T_{10}$, not $S_{10}$.