IB Math Studies Yr 1

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6-2 Arithmetic Sequence Practice

Today’s Learning Goals:

#1 How do we Examine and Use Arithmetic Sequences?

Warm-Up:

1. In an arithmetic sequence, 𝑢4 = 19 and 𝑢7 = 31. a. What is the common difference of this sequence?

b. Determine the formula for 𝑢𝑛, the term of this sequence.

c. Calculate the 27th term of this sequence.

Let’s Extend our Thinking:

d. What term is 203?

Steps to our thinking:

1. This question is giving us:

2. We need to solve for:

IB Math Studies Yr 1

When asked to find n given a term:

1. Find the common difference

2. Write down the nth term of the sequence (the formula)

3. Plug in the given term value for Un

4. Solve for n.

You Try:

2. Consider the arithmetic sequence 1, 5, 9, 13, …

a. Find the common difference.

b. Write down the nth term of the sequence.

c. What is the 41st term of the sequence?

d. Which term of the sequence is 397?

IB Math Studies Yr 1

Taking it a step further

When asked to find the number of terms in a finite sequence:

1. Find the common difference

2. Write down the nth term of the sequence (the formula)

3. Plug in the last term value for Un 4. Solve for n.

Together: 3. Consider the following sequence:

57, 55, 53 ..., 5, 3

a. Find the number of terms of the sequence.

You try 4. Consider the following sequence:

36, 40, 44 … 172

a. Find the common difference

b. How many terms are in this finite sequence.

IB Math Studies Yr 1

Working backwards to find the first term: 1. Draw out a list of the sequence with blanks and term numbers

2. Find the common difference using the slope method (if necessary)

3. Work backwards to find U1

4. Write the general term and follow through with the remaining questions

Together: 5. The fifth term of an arithmetic sequence is 20 and the twelfth term is 41.

a. Find the common difference.

b. Find the first term of the sequence.

c. Calculate the eighty-fourth term.

You Try:

6. The tenth term of an arithmetic sequence is 32 and the common difference is –6.

a. Find the first term of the sequence.

b. Find the 21st term of the sequence.

IB Math Studies Yr 1 Name_____________________________

Date _____________________________

Lesson 6-2: Homework:

**Use your notes from today’s lesson to help you with the following examples.**

1. The first term of an arithmetic sequence is 3 and the seventh term is 33.

a. Calculate the common difference;

b. Calculate the 95th term of the sequence;

2. Sequence B is shown below.

a. Write down the nth term of the sequence.

b. Calculate the 55th term of the sequence.

c. What term of the sequence is 250?

IB Math Studies Yr 1

3. An arithmetic sequence has the following terms: 𝑎3 = 94 𝑎𝑛𝑑 𝑎7 = 86.

a. Calculate the common difference for this sequence.

b. Write down the 1st term of the sequence.

c. Calculate the 50th term.

4. Consider the arithmetic sequence 326, 321, 316, 311, …, 191.

a. Find the value of the common difference of this sequence.

b. Find the number of terms in this sequence.