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SequencesBy the end of this lesson you will:

- find the nth term for linear sequences- use the nth term to find any term in a sequence

Tracking BGrade C / B

Key words: sequences, nth term, linear, difference

Write down the first 4 terms foreach sequence...

a)2nb)2n + 1

c)2n + 5d)2n 3e)- 2nf)4 2n

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Can you suggest why they are called linear sequences?

1 2 3 40 5

2

4

6

8

10

tn= 2n + 1

tn= 3n - 4

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5

811

14

17

?

A linear number sequence is a sequence of numbers that has aconstant difference between adjacent terms. Consider the first fiveterms of the number sequence shown:

5, 8, 11, 14, 17,..?1st 2nd 3rd 4th 5th ................................nth

Can you see how the numbers of thissequence are related to those in the 3 timestable?

n 3n

1 3

2 63 9

4 12

5 15

3n + 2

Adjacent numbers in the 3 times table alsodiffer by 3. The terms in this sequence are 2bigger than the numbers in the 3 times table.

tn= 3n + 2

+ 2

terms

position

3 3 3 3difference

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Question 1

For each of the number sequences below, find a rule for the nth term (tn) and work out the value of t100 .

8, 13, 18, 23, 28,

tn= 5n + 3 t100 = 5 x 100 + 3 = 503

Question2

1, 4, 7, 10, 13, tn= 3n - 2 t100 = 3 x 100 - 2 = 298

Question

3

2, 9, 16, 23, 30, tn= 7n - 5 t100 = 7 x 100 - 5 = 695

Question4

9, 15, 21, 27, 33,

tn= 6n + 3 t100 = 6 x 100 + 3 = 603

Question

5

-1, 4, 9, 14, 19, tn= 5n - 6 t100 = 5 x 100 - 6 = 494

Question6

-3, 1, 5, 9, 13, tn= 4n - 7 t100 = 4 x 100 - 7 = 393

Question7

6, 18, 30, 42, 54,

tn= 12n - 6 t100 = 12 x 100 - 6 = 1194

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Number sequences can beused to solve problemsinvolving patterns indiagrams.

How manysquares of

chocolate (S) will

the 10th

diagram(D) contain?1

2

3

4

1 3 5 7

S = 2D - 1 S10 = 2 x 10 - 1 = 19

How many wooden braces (B) will there be, in the 20th panel (P)?

1 2 3

B = 3P + 1 B20 = 3 x 20 +1= 61

4 7 10

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How many stoneslabs (S) will the15th diagram (D)

contain?

1

2

3

1 5 9

S = 4D - 3 S15 = 4 x 15 3 = 57How many steel braces (B) will there be, in the 28th panel (P)?

1 2 3

6 11 16

B = 5P + 1 B28 = 5 x 28 + 1 = 141