Explore linear sequences, nth term calculations, first and second differences, square numbers, and value determinations in a series of mathematical questions displayed on whiteboards for interactive learning. Get insights into pattern recognition, sequence progression, and second difference calculations.
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Presentation Transcript
Friday, 04 July 2025 Linear Sequences Revision 6 3 9 12 15 11 20 8 14 17 +3 +3 +3 +3 These are called the first differences This sequence is the three times table add five 3n + 5
Friday, 04 July 2025 On your whiteboards What is the nth term? 2 4 6 8 10 10 16 8 12 14 +2 +2 +2 +2 2n + 6
Friday, 04 July 2025 On your whiteboards What is the nth term? 10 20 30 40 50 18 48 8 28 38 +10 +10 +10 +10 - 2 10n
Friday, 04 July 2025 On your whiteboards What is the nth term? -10 -20 -30 -40 -50 -2 -32 8 -12 -22 -10 -10 -10 -10 + 18 -10n
Friday, 04 July 2025 On your whiteboards What is the same? What is different? What is the nth term? 4 16 25 1 9 +3 +5 These are called the first differences +9 +7 These are called the second differences +2 +2 +2
Friday, 04 July 2025 On your whiteboards These are the square numbers. The nth term of this sequence is ?2. The second difference is always constant for a quadratic sequence. 4 16 25 1 9 +3 +5 +9 +7 +2 +2 +2
On your whiteboards Friday, 04 July 2025 Here we have the sequence of 2?2 Work out the value of the second difference 32 50 2 18 8 +6 +10 +18 +14 +4 +4 +4
On your whiteboards Friday, 04 July 2025 Here we have the sequence of 3?2 Work out the value of the second difference 48 75 3 27 12 +9 +15 +27 +21 +6 +6 +6
On your whiteboards Friday, 04 July 2025 Here we have the sequence of 10?2 What do you expect the value of the second difference to be? Are you correct? 40 90 160 250 10 +30 +50 +90 +70 +20 +20 +20
On your whiteboards Friday, 04 July 2025 5?2 What is the nth term? 125 5 45 20 80 +15 +25 +45 +35 +10 +10 +10
On your whiteboards Friday, 04 July 2025 5?2? What is the nth term? 127 7 47 22 82 +15 +25 +45 +35 +10 +10 +10
On your whiteboards Friday, 04 July 2025 What is the nth term? 80 125 5 20 45 127 7 47 22 82 5?2+ 2
Finding the nth term of a quadratic sequence Mark your work In your books: 1) 5?2+ 10 1) 15, 30, 55, 90, 135 2) 5?2 4 2) 1, 16, 41, 76, 121 3) 4?2 3) 4, 16, 36, 64, 100 4) 4?2 2 4) 2, 14, 34, 62, 98 5) 4?2+ ? 5) 5, 18, 39, 68, 105
On your whiteboards Friday, 04 July 2025 5?2 What is the nth term? -80 -125 -5 -45 -20 -15 -25 -45 -35 -10 -10 -10
On your whiteboards Friday, 04 July 2025 5?2? What is the nth term? -75 -120 0 -40 -15 -15 -25 -45 -35 -10 -10 -10
On your whiteboards Friday, 04 July 2025 What is the nth term? -80 -125 -5 -20 -45 -75 -120 0 -40 -15 5?2+ 5
On your whiteboards Friday, 04 July 2025 ?2? What is the nth term? 31 3 13 7 21 +4 +6 +10 +8 +2 +2 +2
On your whiteboards Friday, 04 July 2025 What is the nth term? 16 1 4 9 25 31 3 13 7 21 4 5 6 2 Seq. - ?2 3 ?2+ ? + 1
On your whiteboards Friday, 04 July 2025 2?2? What is the nth term? 55 3 21 10 36 +7 +11 +19 +15 +4 +4 +4
On your whiteboards Friday, 04 July 2025 What is the nth term? 32 2 8 18 50 55 3 21 10 36 3 4 5 1 Seq. - ?2 2 2?2+ ?
Finding the nth term of a quadratic sequence Mark your work In your books: 1) ?2+ ? 1) 2, 6, 12, 20 2) ?2+ 2? 2) 3, 8, 15, 24 3) ?2+4? 3) 5, 12, 21, 32 4) 2?2+ 2? + 2 4) 6, 14, 26, 42 5) 2?2+ 20 5) 18, 12, 2, -12
