Make a T-chart and find a pattern with the difference tests. 1 st level Difference Test. Linear equation with a slope of 2. What needs to be done to 2, 4, 6, 8 to get 1, 3, 5, 7? Alternating signs means we have (-1) n-1 power. 2 nd level Difference Test. Quadratic equation What needs to be done to 1, 4, 9, 16 to get 2, 5, 10, 17?

Do you see a pattern?

The k values are 1 bigger than the powers on the 2.

Notice that all the properties creates summations that all start at k = 1 and ends with n.

Find each sum. Property #2 and #6. n = Property #3.Property #8. Property #1.

Property #2, #3, and #4. n = Property #7, #6, and #1.

Not k = 1, Property #5 Property #2.Property #5. n =

1 st level difference test. +4 d = 4 a 1 = 2 a 40 = 2 + 4(40 – 1) a 40 = 2 + 4(39) = 158 n = 40 Treat the terms like points, as we did in Sect. 9.1, ( 4, 20 ) and ( 13, 65 ). The difference, d, is the same as the slope. Find the slope between the 2 points. Find a 1, use ( 4, 20 ) and ( 1, a 1 ) with the slope formula.

This is a visual approach to solving this problem. Make consecutive blanks for each term. ____, ____ a1a1 Make an equation from 20 to 65 with the 9 d’s. Now subtract the d value backwards for the 1 st term.

times how many groups? 101 ( 50 ) = 5050 Build the formula. Where did the numbers come from? These two formulas go hand in hand. na1a1 a 150 = ? +11 d = 11 a1a1 anan n = ? d = -50 Solve for n. Find these values.

*3 r = 3 a1a1 n = 10 ____, ____ Make an equation from 36 to 16 with the 2 r’s. With two r values gives us 2 equations.

Multiply both sides by a –r. This creates opposite terms. Add the equations together and cancel terms. Factor out the S.Factor out the a 1 Divide by (1 – r). a 1 = 5n = 10 r = 2

? ( ½ ) oo will continue to get smaller until it is zero! Dividing by ( ½ ) is the same as multiplying by the reciprocal of 2.

Determine when a series diverge or converge. If a finite sum approaches a number L as, we say the infinite geometric series converges. A series diverges when the sum is. An infinite geometric series will always converge when. This gives us two formulas for geometric series. An infinite geometric series will always diverge when.

2 nd STAT – OPS #5 is the sequence formula. seq(function,variable,starting value,ending value) Find the first 5 terms of 2 nd STAT – MATH #5 is the sum formula. Used for Series questions. sum(seq(function,variable,starting value,ending value)) Find