Question

4) a) Write down an arithmetic sequence with common difference 8 ?

b) Can the difference between any two terms of this sequence be 70 ? Why ?) ​

Answer 1

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Answer 2

Rule

We can write an Arithmetic Sequence as a rule:

xn = a + d(n−1)

(We use "n−1" because d is not used in the 1st term).

Example: Write a rule, and calculate the 9th term, for this Arithmetic Sequence:

3, 8, 13, 18, 23, 28, 33, 38, ...

This sequence has a difference of 5 between each number.

The values of a and d are:

a = 3 (the first term)d = 5 (the "common difference")

Using the Arithmetic Sequence rule:

xn = a + d(n−1)

= 3 + 5(n−1)

= 3 + 5n − 5

= 5n − 2

So the 9th term is:

x9 = 5×9 − 2

= 43

Is that right? Check for yourself!