Terms
What is the difference between a common difference and a common ratio?
Common difference: the difference between successive terms in an arithmetic sequence d=tn-tn-1
Common ratio: the ratio of successive terms in a geometric sequence r=tn/tn-1
Determine T30 and n when Tn=162
sequence: 18,27,36,45
T30=279
T17=162 (n=17)
What is T19 in the following sequence?
2,6,18
T19=774,840,978
What is the Sum of the 31th term in this series?
2+6+10+14...
The Sum of the 31st term is 1,922.
A car travels 300 m the first minute, 420 m the next minute, 540 m the third minute, and so on.
What’s the total distance the car travels in 5 minutes?
2700m
What is the difference between a sequence and a series?
Sequence: An ordered list of elements
Series: A sequence in which the terms are summed, not just listed.
d= 3
T1= 18
Find T5
T5=30
Determine a formula for the nth term for
1)r=3 and T1=3
Tn=3(3)n-1
What is the Sum of the 7th term in this series?
3+12+48...
The Sum of the 7th term in this series is 16,383.
For a fitness program an athlete jogs 12 minutes her first week and each week after increases her run by 6 minutes. How many weeks will it be by the time she is running 60 minutes per day?
9 weeks
What is a general term?
What is the general term of the sequence 48, 36, 24?
An expression for directly determining any term of a sequence?
What is tn=-12n+60
__, 7,__, __, 31
Find T1, d and T12
What is...?
T1= -5
d= 12
T12= 127
Find T20
350, -262.5, 196.875
T20=1.5
The Sum of the 5th term in an arithmetic series is 65 and T1=3, what is T13?
T13=63
In the math world, a paper airplane is thrown in the air. The plane rises up 5m and goes down 5m again. For every dip, it rises 0.75 its previous dip. What is the total vertical distance the plane travels?
S=40m
What is the difference between and geometric sequence and a geometric series?
Geometric Sequence: A sequence in which the ratio of consequence terms in constant.
Geometric Series: The terms of a geometric sequence expressed as a sum.
T1= 1/2
T18=43/4
Find d and find n when Tn=9.5
d=1/4 (0.25)
T37=9.5
Find T9 in the following geometric sequence
-3,9,-27
T9=-19,683
If the Sum of a nth term in an arithmetic series is 493, Tn= 53 and T1=5, what is n and T13?
n=17
T13=41
Although this is an unrealistic problem... Cheri loves shoes. On the first day of Spring Break, she decides to start cleaning out her closet. If Cheri had 100 pairs of shoes before the first day and each day she got rid of three pairs, how many days would it take for her to only have 7 pairs left? If her husband decides to divorce her on her 12th day of cleaning when she still has too many shoes, how many pairs of shoes will she have?
On the 31st day Cheri will have 7 pairs left
She'll have 64 pairs of shoes when they split up
Under what circumstances will an infinite geometric series converge?
When
|r|<1
Find T2 and T13 when T1=8 and T5=90
T2=28.5 abd T13=254
3y+1, 2y+4...
What is y if r=2?
y=1/2 (0.5)
A ball is dropped from a height of 30 m. The ball rebounds to one quarter of its previous height each time it bounces. I the ball keeps bouncing, what is the total vertical distance the ball travels?
S=50m
Brian has a muffin problem. Every time he goes to the bakery he buys double of what he got the day before. If the first day he went to the bakery and got 3 muffins, how many muffins will he buy on the 7th day? If one muffin is 3$, how much money will he spend on the 10th day? After Brian spends a lot of money in total at the Bakery on the 12th day, the workers get Brian mental help. How much money will he have spent in total by then.
He will buy 192 muffins.
On the 10th day, Brian will spend 4,608$ at the Bakery...
On the 12th day Brian will get mental health assistance for spending 36,855$