UNIT 12.1. Patterns and Algebra

This unit focuses on different methods of solving real-life problems through the following topics- sets, sequences and series, binomial theorem and determinants.

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Topic 6: Sequence and series -Arithmetic Sequence

Subtopic 1 : Terms of Arithmetic sequence

Of the many kinds of sequences and series in this section we shall discuss only the arithmetic sequence.

You will be looking at the terms of an arithmetic sequence.

An Arithmetic sequence, often called an arithmetic progression (AP), is a sequence in which each term after the first differs from the previous term by a constant amount. This amount is called the common difference or simply the difference and is represented by the letter ‘d’.

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Learning outcome:

After completing this topic, you will be able to:1. Identify the arithmetic sequence

2. Find the nth terms in an arithmetic sequence or

progression

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Read and understand the notes below.

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Study the given example on identifying Arithmetic Sequence.

Example:

Determine if the sequence could be arithmetic. If so, give the common difference.

8, 13, 18, 23, 28, …

Study these examples carefully on finding the terms of an infinite Arithmetic Sequence.

Example 1:

Write the five terms of an infinite arithmetic sequence having first term a1 = 3 and common difference d = 2.

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Example 2

Find the 12th term of the arithmetic sequence -9, -5, -1, 3, …

Now lets look at an example on word problem.

Example 3

A rock dislodged by a mountain climber falls approximately 16 feet during the first second, 48 feet during the second second, 80 feet during the third second and so on. Find the distance it falls during the tenth second.

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PRACTICE Refer to the notes on slide 4 and examples on slide 5 and 6

to answer these questions.

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3. With the given information about arithmetic sequence, find the indicated unknown.

i. Given: a1 = 6, d = 3 ii. Given: a2 = 3 , a4 = 7, iii. Given: a2 = 3 , a4 = 5,

Find a5 Find: d; a1 Find: d; a1

4. In arithmetic sequence with a difference of 8, the 4th term is 35. What term is 115?

5. Jane planted 25 marigold saplings in the first row of her garden patch, 24 saplings in the second row, 23 saplings in the third row and so on in an arithmetic sequence. How many saplings will you find in each of the next three rows?

6. A car manufacturing unit produced 550 cars in April, 675 cars in May, 800 cars in June and so on in an arithmetic sequence. Find the number of cars that were rolled out in July, August and September respectively.

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