# Geometric Sequences

## An exercise on geometric sequences including finding the nth term and the sum of any number of terms.

##### LinearLevel 1Level 2Level 3Exam-StyleDescriptionHelpMore

This is level 3: mixed questions about geometric sequences and their sums. You can earn a trophy if you get at least 7 questions correct and you do this activity online.

 Find the sum of the first six terms of the geometric series that begins:2, 4, 8, 16... Find the sum of the first ten terms of the geometric series that begins:6, 18, 54, 162... A geometric sequence has 5 as its first term. The common ratio is two. Calculate the sum of the first eight terms of this sequence . A geometric sequence has 6 as its first term. The common ratio is one third. Calculate the sum of the first ten terms of this sequence giving your answer correct to three significant figures. A geometric sequence has first term 3 and fourth term 24. Calculate the sum of the first five terms of this sequence. A geometric sequence has first term 20 and fourth term 2.5. Calculate the sum of the first five terms of this sequence. Find X if X = 2 + 4 + 8 + 16 + ... + 8192 Find Y if Y = - 32 + 16 - 8 + 4 - 2 ... -½ A geometric sequence has first term 16 and common ratio ½. The sum of the first n terms of the sequence is 31. Find n. A geometric sequence has first term 4 and common ratio 2. The sum of the first n terms of the sequence is 65532. Find n.
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This is Geometric Sequences level 3. You can also try:
Arithmetic Sequences Level 1 Level 2 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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## Answers

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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 - Mixed questions about geometric sequences and their sums

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.

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 Sn=u1(rn-1) ÷ (r-1)

The excellent video above is from Corbettmaths.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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