← Essential Mathematics / 1 Numbers and Algebra
1.4 Sequence and series 2
Essential Mathematics · Grade 11 · 26 lessons in the design
What you will be able to do
- determine the missing term in a number sequence
- determine the first term and the common difference of an arithmetic sequence or series
- determine the nth term in an arithmetic sequence in different situations
- calculate the sum of n terms of an arithmetic progression
- determine the nth term of a geometric sequence
- calculate the sum of a geometric progression
- apply arithmetic and geometric progressions in real life situations
- value the use of sequence and series in day to day life
Key questions
“Where can sequences be applied in real life?”
“How do we find the nth term and the sum of a progression?”
Lessons
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Number sequences
40 min · 1 practice tasks · quizRecognise a sequence, name its terms by position and use the term-to-term rule.
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Finding a missing term
40 min · 1 practice tasks · quizFind a missing term in a sequence by first working out the common step.
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Arithmetic sequences
40 min · 1 practice tasks · quizIdentify an arithmetic sequence and work out its common difference.
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The nth term of an AP
40 min · 1 practice tasks · quizUse Tn = a + (n - 1)d to write a rule for any arithmetic sequence.
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Finding any term
40 min · 1 practice tasks · quizUse the nth term formula to find a high-numbered term of an AP.
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First term and common difference
40 min · 1 practice tasks · quizFind a and d when two terms of an arithmetic sequence are given.
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Two terms give the rule
40 min · 1 practice tasks · quizFind a and d from any two terms, not only the first, using subtraction.
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Arithmetic means
40 min · 1 practice tasks · quizInsert arithmetic means between two numbers to build an AP.
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Sum of an AP
40 min · 1 practice tasks · quizAdd the terms of an arithmetic progression by pairing them.
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The sum formula
40 min · 1 practice tasks · quizWork out the sum of an AP from the first term and common difference.
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Sum of counting numbers
40 min · 1 practice tasks · quizFind the sum of the first n counting numbers using a special case of the AP sum.
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How many terms?
40 min · 1 practice tasks · quizFind the number of terms in an AP by solving the nth term equation.
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Seats in rows
40 min · 1 practice tasks · quizApply the AP sum to rows of seats that grow by a fixed number.
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A savings plan
40 min · 1 practice tasks · quizApply the AP sum to savings that increase by a fixed amount each month.
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Stacking objects
40 min · 1 practice tasks · quizApply the AP sum to objects stacked so each row has one fewer.
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Geometric sequences
40 min · 1 practice tasks · quizIdentify a geometric sequence and work out its common ratio.
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The nth term of a GP
40 min · 1 practice tasks · quizUse Tn = a r^(n - 1) to write a rule for any geometric sequence.
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Finding a GP term
40 min · 1 practice tasks · quizUse the GP nth term formula to find a high-numbered term.
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a and r in a GP
40 min · 1 practice tasks · quizFind the first term and common ratio when two terms of a GP are given.
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Geometric means
40 min · 1 practice tasks · quizInsert geometric means between two numbers to build a GP.
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Sum of a GP
40 min · 1 practice tasks · quizFind the sum of a finite geometric progression using its formula.
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Sum when r is less than 1
40 min · 1 practice tasks · quizUse the alternative GP sum formula when the common ratio is between 0 and 1.
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Growth
40 min · 1 practice tasks · quizApply the GP nth term to population and other percentage growth.
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Depreciation
40 min · 1 practice tasks · quizApply the GP nth term to a value that falls by a fixed percentage each year.
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Compound savings
40 min · 1 practice tasks · quizApply the GP nth term to a savings balance that earns compound interest.
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Sequences: mixed review
40 min · 1 practice tasks · quizBring together arithmetic and geometric progressions and choose the right tool.