Geometric Sequences

An exercise on geometric sequences including finding the nth term and the sum of n terms.

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This is level 1: find the next term of these geometric sequences. You will be awarded a trophy if you get at least 9 answers correct and you do this activity online.

 1 3, 12, 48, ... ☐ ☐ ✓ ✗ 2 6, 12, 24, ... ☐ ☐ ✓ ✗ 3 4, 12, 36, ... ☐ ☐ ✓ ✗ 4 9, 63, 441, ... ☐ ☐ ✓ ✗ 5 15, 90, 540, ... ☐ ☐ ✓ ✗ 6 7, -49, 343, ... ☐ ☐ ✓ ✗ 7 10, -80, 640, ... ☐ ☐ ✓ ✗ 8 -12, 108, -972, ... ☐ ☐ ✓ ✗ 9 -24, -12, -6, ... ☐ ☐ ✓ ✗ 10 -14, 7, -3.5, ... ☐ ☐ ✓ ✗ 11 -28, 252, -2268, ... ☐ ☐ ✓ ✗ 12 -21, 273, -3549, ... ☐ ☐ ✓ ✗
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This is Geometric Sequences level 1. You can also try:
Arithmetic Sequences Level 2 Level 3 Level 4 Level 5 Quadratic Sequences

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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Description of Levels

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Level 1 - Find the next term of these geometric sequences

Level 2 - Find a given term of these geometric sequences

Level 3 - Find the first five terms of the sequence given the formula

Level 4 - Mixed questions about geometric sequences and their sums

Level 5 - Sum of infinite convergent geometric sequences

Missing Terms - Find the missing terms of arithmetic, geometric and Fibonacci-type sequences in this self marking quiz.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Arithmetic Sequences - A similar exercise on arithmetic sequences.

Sigma - Practise using the sigma notation to find the sum of various number series.

More on this topic including lesson Starters, visual aids and investigations.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Geometric Sequences

Here is a reminder of some facts that may help you answering the questions in this exercise.

An geometric sequence, sometimes called a geometric progression, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed number called the common ratio. For example, the sequence 5, 10, 20, 40, ... is a geometric sequence with common ratio 2.

The first term of the sequence can be written as u1

The nth term of the sequence can be written as un

The common ratio is usually written as r

The formula for finding the nth term is un=u1r(n-1)

The formula for finding the sum of $$n$$ terms is:

$$S_n = \dfrac{u_1(r^n-1)}{r-1}$$

The sum of an infinite geometric sequence is:

$$S_\infty = \dfrac{u_1}{1-r}, \quad |r| \lt 1$$

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