Worksheet Sequence Do 1 3 5 6 1

Worksheet: Sequence Do 1 -3, 5, 6 1) A common difference between consecutive terms. 2) Subtract to find d. d = 12 – 7 = 5 a 1 = a 2 - d = 7 – 5 = 2 3) The fourth term of an a. s. is 15. The common difference is 2. Write a formula for the nth term. 15 -2=13 13 -2 = 11 11 -2=9

5) d= 8 -3 = 5 d = 13 -8=5 d= 23 -18= 5 6) 5(2 i+3) 5(2(1)+3)=25 5(2(2)+3)=35 5(2(3)+3)=45 5(2(4)+3)=55 25+35+45+55 = 160

Worksheet: Sequence 4) The second term of an arithmetic sequence is 10. The eleventh term is 37. What is the sixth term? The method: a) Subtract the terms: 37 -10=27 b) Subtract the index values: 11 -2=9 c) Create the ratio to find d: 27/9=3 d) Find a 1 = 10 – 3 = 7 e) Write an = a 1 +(n-1)d f) Find a 6 Do 22 -27

22) d=-5 a 2 = 12 d = a 2 - a 1 -5 = 12 – a 1 -17 = -a 1 = 17 23) 3 rd 4 th 5 th 6 6+3= 9 9+3=12 12+3=15

24. d = -2 By definition 4 th 1 5 th 1 -2= -1 6 th -1 -2=-3 7 th -3 -2= -5 8 th -5 -2= -7 9 th -7 -2=-9 10 th -9 -2= -11 By formula 10 -4=6 1+6(-2)=-11

25. 30, 20, 10, 0, -10 26. 1, 6, 11, 16, 21, 26 27. th 7 2 -9=-7 th 6 -7 -9= -16 5 th -16 -9= -25 4 th -25 -9=-34 3 rd -34 -9= -43 nd 2 -43 -9=-52 st 1 -52 -9=-61

Explicit or Recursive • An explicit form asks you to plug in a number for a variable and get an answer. You can use the same formula for different values. y=2 x an = n + 5 • A recursive form requires that you calculate or know a previous value to get the next value. an = an-1 + 5

Let’s see something • Is 3+5 =5+3? • So 3+10+17+24+31+38= • 38+ 31+24+17+10+ 3? • S 6=6*41 where 41= first value + last value

Formula for a partial sum

Try • Find the sum of the first 50 positive integers. • Find the sum: 7, 14, 21…. 98 • Find the sum: 10, 4, (-2), (-8)…. (-50)

Sum of a Geometric Series With r not equal to 1!