Sequence — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught

An ordered list of numbers. The nth one is an.

Taught in Algebra I · Grade 9 or accelerated Grade 8.

Where it is taught

What uses it later

This idea is needed for:

Practise this idea

8 questions in the course bank use Sequence, in Representing Other Algebraic Relationships, Congruence & Sequences of Transformations, Writing & Transforming Linear Functions, Exponential Functions & Growth, Sequences, Explicit & Recursive.

Problem 1

A sequence goes 3, 8, 15, 24, 35, …. Find the 6th term.

Worked answer

48

Differences: 5, 7, 9, 11, so the next difference is 13

35 + 13 = 48

The rule is n(n + 2): at n = 6, 6 × 8 = 48 ✓

Problem 2

Which sequence guarantees the image is congruent to the original?

  1. Reflect, then translate
  2. Dilate by 2, then translate
  3. Reflect, then dilate by 3
  4. Dilate by 12, then rotate
Worked answer

Reflect, then translate

Reflections and translations are both rigid

Dilations are not, unless k = 1

So the first sequence is the only one

Problem 3

A figure and its image have opposite orientations. Which sequence could have produced it?

  1. A reflection followed by a translation
  2. Two rotations
  3. A translation followed by a rotation
  4. Three rotations
Worked answer

A reflection followed by a translation

Rotations and translations keep the orientation

An odd number of reflections reverses it

So the answer must contain exactly one reflection

Problem 4

Find the common difference of 20, 17, 14, 11, ….

Worked answer

-3

17 - 20 = -3

The sequence is decreasing

Problem 5

Find the 6th term of the geometric sequence 2, 6, 18, ….

Worked answer

486

2 · 35

= 2 × 243 = 486

Problem 6

The graph of a sequence is

  1. a set of separate points
  2. a continuous line
  3. a smooth curve
  4. a shaded region
Worked answer

a set of separate points

Only the counting numbers

So the graph is separate dots

Never join them

Problem 7

A geometric sequence has a1 = 5 and a4 = 135. Find r.

Worked answer

3

5r3 = 135

r3 = 27

r = 3

Problem 8

A geometric sequence has a2 = 12 and a5 = 324. Find a1.

Worked answer

4

12r3 = 324, so r3 = 27 and r = 3

a1 = 12 ÷ 3

= 4

Elsewhere

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