10. 1 Math Practice
What is d in the sequence formulas?
It's the common difference
What is the b in the geometric formula?
It's the common ratio
What is n in the (n-1) part of the sequence formulas?
It's the term position
for geometric sequence, the first term is 8 & the common ratio is 3. Find the 5th term of this sequence.
Start off with making the formula a5= 8(3)^5-1 Then enter this into the calculator 8(3)^5-1 =648 So the 5th term is 648
What is a1 in the sequence formulas?
The first term
Write a formula & write the nth term 42nd term: 5, 12, 19...
The first term is 5 and the common difference is 7. The formula is an=5+(n-1)(7) To find the 42nd term put this in the calculator 5+(42-1)(7) =292 so a42= 292
Write a formula & write the nth term 14th term: a1=4.2; d=-5
The formula is an= 4.2+(n-1)(-5) To find the 14th term put this in the calculator 4.2+(14-1)(-5) =-60.8 so a14= -60.8
Create an equation & find the 12th term. 5, 10, 20, 40...
The formula is an= 5(2)^n-1 To find the 12th term: a12= 5(2)^12 put this in the caculator 5(2)^12-1 =10240 so a12= 10240
Create an equation & find the 10th term 32, 48, 72, 108...
Use the equation an=32(1.5)^n-1 To find the 10th term use a10= 32(1.5)^10-1 Put 32(1.5)^10-1 in the calculator =1230. 1875 so a10= 1230. 1875
How do you find the common ratio?
You divide backwards
Is this arithmetic or geometric? 0, 0.7, 1.4, 2.1...
It's arithmetic, the common difference is 0.7!
Is this arithmetic or geometric? -16, 4, -1, 1/4...
It's geometric, the common ratio is -1/4!
Is this geometric, neither or arithmetic? -2, -4, -12, -48, -240...
It's neither it doesn't have a common ratio or a common difference.
What's a sequence?
A list of numbers that form a pattern.
What's a arithmetic sequence?
A sequence that differs by a common difference.
What's a geometric sequence?
A sequence that differs by the same ratio.
Is this arithmetic or geometric? 12, 8, 4, 0...
Arithmetic! The common difference is -4!
Is this geometric or arithmetic? -11, -19, -27, -35, -43...
Arithmetic, the common difference is -8. -11, -19, -27, -35, -43... ^ ^ ^ -8 -8 -8
Is this geometric or arithmetic? 1, -6, 36, -216, 1296...
Geometric 1, -6, 36, -216, 1296... ^ ^ ^ -7 +42 -216 ^ +49
Is this geometric or arithmetic? 1, 3, 9, 27...
Geometric, the common ratio is 3.
What is the formula for dealing with geometric sequences?
an=a1(b)^n-1
What's the formula for dealing with arithmetic sequences?
an=a1+(n-1)d
-5, 2, 9, 16, 23...
arithmetic, the common difference is +7
