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QLDMath MethodsQuick questions
Unit 1: Algebra, statistics and functions
Quick questions on Arithmetic and geometric sequences and series: QCE Math Methods Unit 1 Year 11
9short 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 general term?Show answer
$T_n = a + (n - 1) d$ where $a$ is the first term.
What is sum of first $n$ terms?Show answer
$S_n = (n/2)[2a + (n - 1) d]$ or equivalently $S_n = (n/2)(a + T_n)$.
What is compound interest?Show answer
Principal $P$ at rate $r$ per period compounded for $n$ periods: $A = P(1 + r)^n$. The amounts form a geometric sequence.
What is exponential growth and decay?Show answer
Population, radioactive decay, drug clearance.
What is annuities?Show answer
Regular payments at compound interest. Formulas based on geometric sums.
What is arithmetic?Show answer
First term 3, common difference 4. Find $T_{10}$ and $S_{10}$.
What is geometric?Show answer
First term 2, common ratio 0.5. Find $S_\infty$.
What is off-by-one in $T_n$?Show answer
Use $n - 1$ in the exponent or multiplier, not $n$.
What is sign errors in $ $ vs $ $?Show answer
Use the form that matches; both are correct but make sure your sign convention is consistent.