I apologize for all these questions but I really need to get them done fast so I appreciate if you tried to answer some of them!

1. Bill is saving money in an empty jar. The first day he puts in a certain amount of money. Every day after the first he puts in 2 more dollars than the amount he put in on the previous day. After 10 days he has put 200 dollars in the jar. How much money did he pit in the jar on the first day?

2. If 45 is the sum of n consecutive positive integers, what is the largest possible value of n?

3. Every hour a clock chimes as many times as the hour. How many times does it chime from 4:00 am throug 11:00 pm of the same day, including 4:00 am and 11:00 pm?

4. 2,3,5,10,11
How many pairs of different numbers can be chosen from the list above so that their product is even? (Note: te pair 2,3 is the same as the pair 3,2)

5. 123...91011...3
If the positive integers are written one after another as shown above until the eighth occurence of the digit 3, how many digits are in the number?

6. If m is the sum of 3 consecutive odd integers, which of the following CANNOT be the value of m? A. 3 B. 15 c. 21 D. 29 E. 45

7. On the first day, Daniel puts one penny into the jr. On the second day he puts 2 pennies into the same jar. On the nth day he pus n pennies into the same jar. Which day is the first day on which he has at least 20 dollars in the jar? (1dollar=100 pennies)

Oh well, number 2

start at 1 for min

1 + 2 + 3 + 4 ..... = 45 arith series

(n/2)[2 + (n-1)(1)] = 45

n + (n/2)(n-1) = 45

n + n^2/2 -n/2 = 45

n + n^2 = 90

n^2 + n - 90 = 0

n = [ -1 +/- sqrt(1+360) ]/2

n = 18/2 = 9

check
1 + 2 + 3 + .....9
= 4.5(2+8) = 45 sure enough

Wow nice explanation thank you! Do you think you could help me with #1 and 5? These two questions are the ones I am most stuck o

#1.

so you have x + (x+2) + (x+4) + .. + (x+18) = 200

( explanation for term(10) = a+9d = x + 9(2) = x+18)

sum(10) = 5(first + last)
5(x + x+18) = 200
2x + 18 = 40
2x = 22
x =11

#5.

visualize the number or write them out
123456789101112131415161718192021222324252627282930313233

Now circle all the 3's. By the time you reach 33, you will have counted 8 3's.
So to write from 1 to 10 took 11 digits
so we have 11 12 ... 33, which is 23 double digits
for another total of 46 digits

you number is 57 digits long

Thank you reiny, makes sense! Can you help me with #5 too? Or the rest is you can?

#6

Let the three consecutive odd numbers be
n, n+2, n+4
their sum = 3n + 6
= 3(n+2)
so the sum is a multiple of 3.
but 29 does not divide evenly by 3,

so it cannot be 29

Oh I see, thank you so much for your help! You are so kind and very good at explaining.