Question

How do you determine if an equation is a geometric sequence, geometric series, arithmetic sequence, or arithmetic series? I have problems in which I have to identify which one they are (WITHOUT SOLVING)... could someone help identify? I will give medals & fans!

Answer 1

My problems:

5. Jackie deposited $5 into a checking account in February. For each month following, the deposit amount was doubled. How much money was deposited in the checking account in the month of August?

6. A local grocery store stacks the soup cans in such a way that each row has 2 fewer cans than the row below it. If there are 32 cans on the bottom row, how many total cans are on the bottom 14 rows?

7. A major US city reports a 12% increase in decoration sales during the yearly holiday season. If decoration sales were 8 million in 1998, how much did the city report in total decoration sales by the end of 2004?

8. A fireplace contains 46 bricks along its bottom row. If each row above decreases by 4 bricks, how many bricks are on the 12th row?

Answer 2

okay so wat is basically a geometric progression?

Answer 3

a progression? is that a sequence?

Answer 4

yes!

Answer 5

so how do you figure out which one is which?

Answer 6

okay so the first thing is the difference between a sequence and a series.
ill give an example for each:
SEQUENCE:
2,4,6,8,10......
this is a sequence where the numbers hav a relation with the first term.
SERIES:
a series is basically the sum of the sequence
2+4+6+8+10....

Answer 7

so sequences deal with multiplication and series deal with addition?

Answer 8

nope sequence isnt a multiplication. its just the grouping of the interrelated data.
NOTE THE COMMA BETWEEN THEM.

Answer 9

data=numbers.

Answer 10

http://mathforum.org/library/drmath/view/61955.html

Answer 11

okay that would make sense. so for the first problem... that would be a series?

Answer 12

yes! :D

Answer 13

geometric or arithmetic?

Answer 14

wat do you think?

Answer 15

...geometric

Answer 16

bullseye!

Answer 17

2nd problem would be a geometric sequence, right?

Answer 18

nope arithmatic sequence!

Answer 19

how do you tell the difference between arithmetic and geometric?

Answer 20

hmm..
ill show the difference between the first and second question

in the first question:-------------------
initially the person deposited $5
then every month the amt. was doubled
so the sequence is
$5,$10($5x2),$20($10x2)......
as every following number is the PRODUCT of the previous number with .....its a GP.
-----------------------------

Answer 21

in the second question:---------------
the bottom row has 32 cans
the next row has 32-2=30 cans
therefore the sequence is
32,30(32-2),28(30-2),......
here every following term is the DIFFERENCE of the previous term and 2.
so its an AP.

Answer 22

ok! so AP deals with the difference and GP deals with the product

Answer 23

AP deals with difference and sums
GP with products

Answer 24

yes you got it
and btw the second question is an arithmatic series

Answer 25

and I have the 3rd as a geometric sequence and the 4th as an arithmetic sequence

Answer 26

im not so sure about the third one but i guess you are right.
and the 4th one is arithmatic sequence. :D
good work XD

Answer 27

awesome! thank you so much! :D

Answer 28

no problem you are welcome! and you are one patient student XDDDD