Linear Sequences Revision

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Mr Barton’s Maths Notes

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Presentation transcript:

Linear Sequences Revision 3 6 9 12 15 8 11 14 17 20 +3 +3 +3 +3 These are called the first differences This sequence is the three times table add five 3n + 5

8 10 12 14 16 2n + 6 What is the nth term? On your whiteboards 2 4 6 8 +2 +2 +2 +2 2n + 6

8 18 28 38 48 10n - 2 What is the nth term? On your whiteboards 10 20 30 40 50 8 18 28 38 48 +10 +10 +10 +10 10n - 2

8 -2 -12 -22 -32 -10n + 18 What is the nth term? On your whiteboards -20 -30 -40 -50 8 -2 -12 -22 -32 -10 -10 -10 -10 -10n + 18

1 4 9 16 25 What is the nth term? On your whiteboards What is the same? What is different? What is the nth term? 1 4 9 16 25 These are called the first differences +3 +5 +7 +9 These are called the second differences +2 +2 +2

1 4 9 16 25 On your whiteboards +3 +5 +7 +9 +2 +2 +2 These are the square numbers. The nth term of this sequence is 𝑛 2 . The second difference is always constant for a quadratic sequence. 1 4 9 16 25 +3 +5 +7 +9 +2 +2 +2

Here we have the sequence of 2𝑛 2 On your whiteboards Here we have the sequence of 2𝑛 2 Work out the value of the second difference 2 8 18 32 50 +6 +10 +14 +18 +4 +4 +4

Here we have the sequence of 3𝑛 2 On your whiteboards Here we have the sequence of 3𝑛 2 Work out the value of the second difference 3 12 27 48 75 +9 +15 +21 +27 +6 +6 +6

10 40 90 160 250 Here we have the sequence of 10𝑛 2 On your whiteboards Here we have the sequence of 10𝑛 2 What do you expect the value of the second difference to be? Are you correct? 10 40 90 160 250 +30 +50 +70 +90 +20 +20 +20

5𝑛 2 5 20 45 80 125 On your whiteboards What is the nth term? +15 +25 +35 +45 +10 +10 +10

5𝑛 2 ? 7 22 47 82 127 On your whiteboards What is the nth term? +15 +25 +35 +45 +10 +10 +10

7 22 47 82 127 5𝑛 2 +2 On your whiteboards What is the nth term? 5 20 45 80 125 7 22 47 82 127 5𝑛 2 +2

Finding the nth term of a quadratic sequence Mark your work 1) 5𝑛 2 +10 2) 5𝑛 2 −4 3) 4𝑛 2 4) 4𝑛 2 −2 5) 4𝑛 2 +𝑛 In your books: 15, 30, 55, 90, 135… 1, 16, 41, 76, 121… 3) 4, 16, 36, 64, 100… 4) 2, 14, 34, 62, 98… 5) 5, 18, 39, 68, 105…

−5𝑛 2 -5 -20 -45 -80 -125 On your whiteboards What is the nth term? -15 -25 -35 -45 -10 -10 -10

−5𝑛 2 ? -15 -40 -75 -120 On your whiteboards What is the nth term? -15 -15 -40 -75 -120 -15 -25 -35 -45 -10 -10 -10

-15 -40 -75 -120 −5𝑛 2 +5 On your whiteboards What is the nth term? -5 -20 -45 -80 -125 -15 -40 -75 -120 −5𝑛 2 +5

𝑛 2 ? 3 7 13 21 31 On your whiteboards What is the nth term? +4 +6 +8 +10 +2 +2 +2

3 7 13 21 31 𝑛 2 +𝑛+1 2 4 5 6 3 On your whiteboards What is the nth term? 1 4 9 16 25 3 7 13 21 31 Seq. - 𝑛 2 2 4 5 6 3 𝑛 2 +𝑛+1

2𝑛 2 ? 3 10 21 36 55 On your whiteboards What is the nth term? +7 +11 +15 +19 +4 +4 +4

3 10 21 36 55 2𝑛 2 +𝑛 1 3 4 5 2 On your whiteboards What is the nth term? 2 8 18 32 50 3 10 21 36 55 Seq. - 𝑛 2 1 3 4 5 2 2𝑛 2 +𝑛

Finding the nth term of a quadratic sequence Mark your work 𝑛 2 +𝑛 2) 𝑛 2 +2𝑛 3) 𝑛 2 +4𝑛 4) 2𝑛 2 +2𝑛+2 5) −2𝑛 2 +20 In your books: 2, 6, 12, 20… 3, 8, 15, 24… 3) 5, 12, 21, 32… 4) 6, 14, 26, 42… 5) 18, 12, 2, -12…

Quadratic Sequences - Extension

Quadratic Sequences - Solution