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Question 34597: This is a problem my mom gave me and it is driving me crazy. I am in the 5th grade and in an advanced math class, but I cannot get this. The problem is to write an algebraic expression that will let me describe a set of data. The data when plotted on a grid has one row of 3 tiles then three rows of 5 tiles then one row of 3 tiles and then three rows of 5 tiles and keps on repeating. So the data in two colums (column one being tiles in next row and column two being the total tiles 'so far) is as follows:
# tiles (Column 1) Total So Far (Column 2)
3 3
5 8
5 13
5 18
3 21
5 26
5 31
5 36
3 39
Can you please help me write an algebraic expression to describe the above data?
Thanks
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! SEE MY COMMENTS BELOW...
This is a problem my mom gave me and it is driving me crazy. I am in the 5th grade and in an advanced math class, but I cannot get this. The problem is to write an algebraic expression that will let me describe a set of data. The data when plotted on a grid has one row of 3 tiles..PUT THE DATA IN A PROPER FORMAT FIRST BASED ON GIVEN DATA.YOUR IDEA OF TABLE IN CLOUMNS AND ROWS IS IN THE RIGHT DIRECTION..BUT YOU MADE SOME ERRORS IN THAT...
ROW NUMBER.....NO.OF TILES....LINKAGE BETWEEN ROW NO.& TILES.. CUMULATIVE TILES
I ROW .........3 TILES.........1*3=3..................................3
then three rows of 5 tiles
II ROW.........5 TILES
III ROW........5 TILES
IV ROW.........5 TILES.........3*5=15 TILES....................1*3+3*5
then one row of 3 tiles
V ROW..........3 TILES.........1*3=3...........................1*3+3*5+1*3
and then three rows of 5 tiles
VI ROW.........5 TILES
VII ROW........5 TILES
VIII ROW.......5 TILES.........3*5=15..........................1*3+3*5+1*3+3*5
and keps on repeating
ETC...ETC....REPEAT..............................1*3+3*5+1*3+3*5+......ETC..
. So the data in two colums (column one being tiles in next row and column two being the total tiles 'so far) is as follows:NOW LOOK FOR A PATTERN .IT IS QUITE CLEAR....WE HAVE 3+15+3+15.......ETC....
WE HAVE A MIXED SERIES.....SO NOW WHAT NEXT?
can you please help me write an algebraic expression to describe the above data?
WHAT IS MEANT BY THIS?
ARE WE TO WRITE HOW MANY TILES ARE IN A ROW ?
OR ARE WE TO WRITE TOTAL HOW MANY TILES ARE USED TILL THAT ROW...OK..LET US DO BOTH?
SINCE IT IS A MIXED SERIES WE CAN HAVE DIFFERENT FORMULAE FOR DIFFERENT STAGES..
R1,R5,R9,R13...ETC...HAVE 3 TILES EACH........THIS IS AN ARITHMATIC SEQUENCE WITH A CONSTANT DIFFERENCE
R1,R5,R9,R13..ETC...CAN BE REPRESENTED BY R(4N-3)WHERE N VARIES FROM 1,2,3,4...ETC..WE GET CORRESPONDINGLY R1,R5,R9,R13
OFCOURSE THE VALUE IS CONSTANT IT IS 3 ALWAYS..THE NUMBER OF ILES IN THAT ROW..
NEXT IS
R2-R4,R6-R8,R10-R12....ETC...HAVE 5 TILES EACH.WITH SAME REASONING AS ABOVE WE CAN SAY FOR R(4N-2),R(4N-1),R(4N)....THE VALUE IS 5 TILES IN EACH ROW..
NEXT IS CUMULATIVE....THIS INVOVES A FORMULA WHICH YOU MAY TAKE IT OR GRANTED NOW AS YOU ARE I ONLY 5 TH. STD.
IF ROW NUMBER IS R(4N-3)....THEN CUMULATIVE NUMBER OF TILES IS
S(4N-3)=3*N+15*(N-1).....YOU CAN CHECK THIS FOR
N=1....S1.....3*1+15*(1-1)=3...GIVES TOTAL UPTO AND INCLUDING ROW NO.1
N=2....S5.....3*2+15(2-1)=21...GIVES TOTAL UPTO AND INCLUDING ROW NO.5
N=3....S9.....3*3+15(3-1)=39....
IF ROW NUMBER IS R(4N-2)....THEN CUMULATIVE NUMBER OF TILES IS
S(4N-2)=3*N+15*(N-1)+5....YOU CAN CHECK THIS FOR DIFFERENT VALUES OF N AS ABOVE.
IF ROW NUMBER IS R(4N-3)....THEN CUMULATIVE NUMBER OF TILES IS
S(4N-1)=3*N+15*(N-1)+10...YOU CAN CHECK THIS FOR DIFFERENT VALUES OF N AS ABOVE.
IF ROW NUMBER IS R(4N-3)...THEN CUMULATIVE NUMBER OF TILES IS
S(4N)=3*N+15*(N-1)+15...YOU CAN CHECK THIS FOR DIFFERENT VALUES OF N AS ABOVE.
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