# Math

posted by Ethan

1. Daniel wants to save at least 20 dollars by putting pennies in a jar daily. On first day, he puts one penny into the jar. 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 thejar? (1 dollar=100 pennies) a. 60 b. 61 c. 62 d. 63 e. 64
I tried the sum equation but I got 1334 which is no one of the choices.

2. The first term of a sequence is 12, and each term after the first is 2 less than the preceding term. If n is a positive integer, which of the following could be the sum of the first n terms of the sequence? a. -14 b. -2 c. 28 d. 31 e. 81

3. "123...91011...3" If the positive integers(to the left) are written one after another as shown until the eighth occurence o the digit 3, how many digits are in the number? a. 29 b. 33 c. 39 d. 48 e. 57

1. Steve

#1
n(n+1)/2 >= 2000
n^2+n-4000 > 0
n > 62.7
So, 63 days

#2 clearly the sum must be even.
sum = n/2 (24+(n-1)(-2))
http://www.wolframalpha.com/input/?i=n%2F2+%2824%2B%28n-1%29%28-2%29%29+for+n%3D1+to+50

#3
1-digit #'s: 3
teens: 13
20's: 23
30's: 30-33

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