Year 12 Maths Advanced MAV-12-03 Checkpoint 1

Checkpoint Quiz 1

This checkpoint covers Geometric Sequences in Finance and Sequences, Series and Sigma Notation (Lessons 1–2).

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Quick Review

Compound interest as a GP: balances form a geometric sequence with first term $a = P(1+i)$ and common ratio $r = (1+i)$, so $T_n = P(1+i)^n$. The ratio is never just the interest rate $i$.
Reducing balance depreciation: book values form a GP with common ratio $r = (1-d)$, where $d$ is the depreciation rate. Because $r < 1$, values shrink each period.
$T_n$ vs $S_n$: $T_n$ is a single balance at period $n$; $S_n = \dfrac{a(r^n-1)}{r-1}$ is the sum of all balances up to period $n$. Confusing the two is a common exam trap.
Sequences and series: a sequence is an ordered list of terms $T_1, T_2, T_3, \ldots$; a series is the sum of those terms, with partial sum $S_n = T_1 + T_2 + \cdots + T_n$.
Sigma notation: $\displaystyle\sum_{k=r}^{n} T_k$ compresses a sum into one expression. The identity $T_n = S_n - S_{n-1}$ (for $n \geq 2$) recovers a term from consecutive partial sums, always check $T_1 = S_1$ separately.

5 random questions from the Checkpoint 1 bank, feedback shown immediately

Great work finishing Checkpoint 1.

If you struggled with any questions, go back to Lessons 1–2 to review the concepts before moving on.

Tick when you're ready to continue to Lesson 3.