Math 130

Sum the first two odd numbers, then the first three, the first four, and so on. From these observations could you guess the sum of the first 100 odd numbers?

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  1. 1+3=4
    1+3+5=9
    1+3+5+7=16
    notice it goes like this:
    first two = 2^2
    first three=3^3
    first four= 4^2
    first 15=15^2
    first hundred= ???

  2. How many four-digit numbers abcd exist such that a is even, b is divisible by 5, c is prime, and d is odd?

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  3. Find the smallest values for a and b so that 21 base a equals 25 base b.

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