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Warm Up: Find the following sums

Warm Up: Find the following sums. 1. . 2. . 3. . 4. . Sequences. Sometimes it is relatively easy to find the pattern of a sequence. and sometimes it is a little more difficult. Finding Successive Differences. 74. 14 22 32 44 58 ___. 8 10 12 14 .

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Warm Up: Find the following sums

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  1. Warm Up: Find the following sums 1. 2. 3. 4.

  2. Sequences Sometimes it is relatively easy to find the pattern of a sequence and sometimes it is a little more difficult

  3. Finding Successive Differences 74 14 22 32 44 58 ___ 8 10 12 14 16 2 2 2 2

  4. Finding Successive Differences 202 2 6 22 56 144 ___ 4 16 34 58 88 30 12 18 24 6 6 6

  5. Find the next term in the sequence 235 5 15 37 77 141 ___ 10 22 40 64 94 30 12 18 24 6 6 6

  6. Sums of Numbers Recall that we were able to quickly find the sum of consecutive integers by using the Gauss method 1+2+3+…+99+100 = 5050 (100 ÷ 2)(101) =

  7. Sums of Numbers Write a formula for finding the sum of the first n counting numbers 1+2+3+…+(n-2)+(n-1)+n= (n ÷ 2)(n+1) =

  8. Sums of Numbers Here is an interesting way to come up with this formula Let S=1+ 2 + 3 +…+(n-1)+n + S=n+(n-1)+(n-2)+…+ 2 +1 2S=(n+1)+(n+1)+(n+1)+…+(n+1) 2S=n(n+1)

  9. Sums of Odd Counting Numbers See if you can find the sum of odd consecutive counting numbers. Find the sum of the first n odd counting numbers S=1+3+5+7+…+(2n-1) Hint: Try taking a couple of sample sums

  10. Sums of Odd Counting Numbers 1=1 1+3=4 1+3+5=9 1+3+5+7=25

  11. Summary Sum of n consecutive numbers Sum of n consecutive odd numbers

  12. Find the sum of the first n consecutive even numbers S=2+4+6+8+…+2n S=1+2+3+…+(n-2)+(n-1)+n 2S=2(1+2+3+…+(n-2)+(n-1)+n) 2S=2(1)+2(2)+2(3)+…+2(n) 2S=2+4+6+8+…+2n S=2S

  13. S=2S

  14. Figurate Numbers Numbers and sequences of numbers that are formed based on the geometric arrangement of points

  15. Figurate Number Examples

  16. How many dots are in the next figure? 21 6 2 3 4 5 1 1 1 1

  17. How many dots are in the 99th figure? Figure 1 2 3 4 5 … n # of Dots 1 3 6 10 15 … ?

  18. The number of dots in the nth figure is the same as the sum of the first n counting numbers

  19. Homework Sequence, Sums and Figurative Numbers Worksheet

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