Question

MEDAL AND FAN AND GREAT TESTIMONIAL GIVEN :D
PLEASE HELP :)

starting with the second day of school, Jose and his friends traded stamps during recess and lunch. Jose got 4 new stamps that day. On the third day, he got 8 new stamps. On the fourth day, he got 12 new stamps. On the next day, he got 16 new stamps. If the pattern continues, how many new stamps will Jose get on the tenth day? How many new stamps will he have gotten in all?

Answer 1

@satellite73
@mathslover
@jim_thompson5910

Answer 2

@ghazi

Answer 3

any help on any of the attachments will be appreciated :)
Thnx

Answer 4

@satellite73
@saifoo.khan

Answer 5

First term: 4

Common Difference: 8 - 4 = 4, 12 - 8 = 4, etc

So a1 = 4 and d = 4

So you have an arithmetic sequence:

a(n) = a1 + d(n-1)

a(n) = 4 + 4(n-1)

a(n) = 4 + 4n-4

a(n) = 4n

Answer 6

tn= a + (n-1)d
d=4, a= 12 and n=10

Answer 7

the 10th term is

a(n) = 4n

a(10) = 4(10)

a(10) = 40

Answer 8

to find the sum of the first 10 terms, you would use this formula

Sn = n*(a1 + an)/2

Answer 9

wouldn't the 10th term equal 36?

Answer 10

where n = 10, a1 = 4, an = 40 (tenth term)

Answer 11

but it says 4 is in day 2? not day 1?

Answer 12

oh true, so you would use n = 9 because n = 1 refers to day 2

Answer 13

so it would be 36, or not?

Answer 14

yes

Answer 15

and the sum, would it be 180 in total?

Answer 16

correct

Answer 17

oh okaii thanx.
can you help me with #2? maybe?

Answer 18

@jim_thompson5910

Answer 19

Ok I'll help with one more

what did you get for # 2?

Answer 20

oh one more, in that case i need more help in #4

Answer 21

ok so do # 4 instead of # 2?

Answer 22

yes please :)

Answer 23

ok one sec

Answer 24

sure

Answer 25

ok so they switch when the total score is 5 or a multiple of it

so if one side has 3 points and the other side has 2 points, then the total score is 3+2 = 5

Answer 26

which means that the teams would change sides at this point

Answer 27

if the score on one side is 6 and the other side is 4, then 6+4 = 10

the teams would flip sides at this point since 10 is a multiple of 5

Answer 28

oh so the multiple would be if they add to 5 ?

Answer 29

they switch yes, if the sum is 5, 10, 15, etc

Answer 30

can you continue explaining the rest of this problem?

Answer 31

they just want you to make up scores that add up to 5, 10, 15, etc

Answer 32

3+2 = 5
6+14 = 10

are two sets of scores

Answer 33

you could have 1, 4 ---> 1+4 =5

or 0 and 5 ---> 0+5 = 5

or any other combo that adds to 5

Answer 34

then you just make up any final score that's reasonable (within the given limits of this problem)

Answer 35

oh so the final scores have to add up to five?

Answer 36

the final scores could be 15 to 12 since the first team reached 15

Answer 37

another final score could be 27 to 25 since the first team scored 2 more points than the second

Answer 38

but i thought it could not pass 15 since when they reach 15 they change?

Answer 39

if one team reaches 15 then that teams wins if they have more than one point that the other team

Answer 40

so 15 to 12 would have team A winning

but 15 to 14 would mean the game isn't over yet

Answer 41

yeah but you said "another final score could be 27 to 25 since the first team scored 2 more points than the second"?

Answer 42

yes say the score is 26 to 25, the game isn't over

but say team A scores one point to get 27 to 25, the game would be over with team A the winner

Answer 43

oh but if they reach 15 they win, so how did they reach 27?

Answer 44

if it's 15 to 14, the game isn't over

Answer 45

15 to 15, game isn't over
15 to 16, game isn't over
16 to 16, game isn't over
...
...
25 to 25, game isn't over
26 to 25, game isn't over
27 to 25, team A wins

Answer 46

oh okaii ... wait?

Answer 47

what

Answer 48

where are you stuck?

Answer 49

but why would one team have 27 to 25 ? that is past the range of 15 for a team to win?

Answer 50

you can only win if you get to 15 and your team has more than 1 point than the other

Answer 51

15 to 14 would not end the game but 15 to 13 would (team A wins)

Answer 52

yeah but u exceeded 15 when u got 27?

Answer 53

yes i know but you need to be at least 2 points above the losing team

Answer 54

technically, the game could go on forever if you keep tying

Answer 55

so you win if one team get like 15 to 13 right? or like 12 to 10? or even like 22 to 25? am i right?

Answer 56

you have to be at least 2 pts above and be at 15 or greater

Answer 57

12 to 10 the games not over yet

Answer 58

wait why?

Answer 59

because neither team has gotten to 15 yet

Answer 60

22 to 25 would have team B win, but that's not a possible score

Answer 61

22 to 24 would work though

Answer 62

why would it not work?

Answer 63

because 22 to 24 would end the game

Answer 64

22 to 25 isn't possible to reach

Answer 65

why not?

Answer 66

is it cause its +3 more?

Answer 67

yeah but once the score is 22 to 24, the game is over

Answer 68

oh okaii got you so can you help me with #2 please? that is all i need?

Answer 69

no sry, i have to get going

Answer 70

oh, okaii r u going to help others now?

Answer 71

thanx though really appreciate it :)

Answer 72

@satellite73
@ghazi
@mathslover
@abb0t

Answer 73

@satellite73
@sammie12