Warm Up: Find the following sums

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

Finding Successive Differences ___

Finding Successive Differences ___

Find the next term in the sequence ___

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

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

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

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= …+(2n-1) Hint: Try taking a couple of sample sums

Sums of Odd Counting Numbers 1=1 1+3= = =25

Summary Sum of n consecutive numbers Sum of n consecutive odd numbers

Find the sum of the first n consecutive even numbers S= …+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= …+2n S=2S

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

Figurate Number Examples

How many dots are in the next figure?

Figure12345 …n # of Dots … ? How many dots are in the 99th figure?

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

Homework Sequence, Sums and Figurative Numbers Worksheet