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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

5short 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?
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Tn=a+(n−1)dT_n = a + (n - 1) d where aa is the first term.
What are sum of first nn terms?
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Sn=(n/2)[2a+(n−1)d]S_n = (n/2)[2a + (n - 1) d] or equivalently Sn=(n/2)(a+Tn)S_n = (n/2)(a + T_n).
What is compound interest?
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A principal PP at rate rr per period compounded for nn periods grows to A=P(1+r)nA = P(1 + r)^n, and the successive balances form a geometric sequence with common ratio 1+r1 + r. This is the most direct application of geometric sequences in the course.
What is exponential growth and decay?
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Population growth, radioactive decay and drug clearance all change by a constant factor per period, making them geometric and linking directly to the exponential functions studied alongside.
What are annuities and repeated payments?
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A stream of regular payments earning compound interest sums as a geometric series, so the sum formula Sn=arn−1r−1S_n = a\dfrac{r^n - 1}{r - 1} values the whole stream. This idea underpins savings plans and loan repayments met later in the course.

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