MYP 4Year 10Term 1

Sequences

Arithmetic · Geometric · Shifted patterns · Recursive notation

Functions

15 objectives

Learning objectives

What students should be able to do by the end of this unit.

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Represent a sequence using pictures, tables of values, graphs and algebra.
Describe a sequence using a term-to-term rule (in words) and a position-to-term rule (using $n$).
Identify whether a sequence is arithmetic, geometric, quadratic or neither.
Use the general rule of a sequence to predict any $n$th term.
Test whether a given number is a term of a sequence by solving an equation.

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Determine the general rule $u_n = u_1 + (n-1)d$ for an arithmetic sequence.
Determine the general rule $u_n = u_1 \cdot r^{n-1}$ for a geometric sequence.
Work backwards from given terms to find $u_1$, $d$, $r$ or $n$ (e.g. given $u_5 = 2$ and $u_8 = 8$, find $r$).
Use properties of sequences to solve for unknowns (e.g. consecutive arithmetic terms $k$, $2k+2$, $4k+4$; consecutive geometric terms $2$, $k$, $10$).
Write a recursive rule for an arithmetic sequence using $u_{n+1} = u_n + d$.
Write a recursive rule for a geometric sequence using $u_{n+1} = u_n \cdot r$.

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Determine the general rule from a shifted square or cube sequence (e.g. one less than the square numbers gives $u_n = n^2 - 1$).
Calculate the sum of the first $n$ terms of an arithmetic series.EXT
Calculate the sum of the first $n$ terms of a geometric series.EXT
Discuss the behaviour of an infinite geometric series and identify when it converges.EXT

Review pack

Curated revision materials parents and students can download.

A review pack for this unit is being prepared.