How to write down the terms in a sequence using the nth term.

To generate a number sequence using the nth term (that is write down the terms in a sequence) is to substitute the numbers 1, 2, 3,4 and 5 into your nth term. Most questions usually ask for the first 5 numbers of a sequence, but to find other numbers just substitute more numbers into you nth term. Let’s take a look at some examples.

Example 1

The nth term of a number sequence is 4n+3. Write down the first five numbers of the sequence.

All you need to do is substitute the numbers 1 to 5 into your formula.

n = 1

4 × 1 + 3 = 7

n = 2

4 × 2 + 3 = 11

n = 3

4 × 3 + 3 = 15

n = 4

4 × 4 + 3 = 19

n = 5

4 × 5 + 3 = 23

So your first 5 numbers are 7,11,15,19 and 23

Example 2

The nth term of another number sequence is 7n – 2.

Part A: Write down the first 5 numbers of this sequence. Part B: Also work out the 90th term in the number sequence.

Part A

Again, substitute n=1 to 5 into your nth term.

n = 1

7 × 1 – 2 = 5

n = 2

7 × 2 – 2 = 12

n = 3

7 × 3 – 2 = 19

n = 4

7 × 4 – 2 = 26

n = 5

7 × 5 – 2 = 33

Part B

To find the 90th term in the numbers sequence, all you need to do is substitute n = 90 into your nth term. So 7 multipled by 90 is 630 (ignore the zero and add it on), and 630 take away 2 is 628.

Example 3

The nth term of another sequence is 6n-3. Write down the 70th term of this number sequence.

All you need to do this time is substitute n = 70 into your nth term.

This gives:

6 × 70 -3 = 417

Summary

To find the terms in a number sequence substitute the numbers 1 to 5 into your formula. To find other numbers just substitute the value into your formula (swap n for your number).

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