SOLUTION: Take a look at the following sums: 1=1 1+3=4 1+3+5=9 1+3+5+7=16 1+3+5+7+9=25 a. Come up with a conjecture about the sum when you add the first n odd numbers. For examp

Question 1046328: Take a look at the following sums:
1=1
1+3=4
1+3+5=9
1+3+5+7=16
1+3+5+7+9=25
a. Come up with a conjecture about the sum when you add the first n odd numbers. For example when you added the first five odd numbers ( 1+3+5+7+9) what do you get? What if I wanted to add the first 10 odd numbers? Or 100?
b. Can you think of a geometric interpretation of this pattern? If you start with one square and add on three more, what can you make? If you now have four squares and you add on five more, what can you make?
c. Is there a similar pattern for adding the first n even numbers?
2=2
2+4=6
2+4+6=12
2+4+6+8= 20
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
1=1
1+3=4
1+3+5=9
1+3+5+7=16
1+3+5+7+9=25
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Regarding the sum of first "n" odd/even natural numbers, see the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Chocolate bars and arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions
in this site.

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`Take a look at the following sums: 1=1 1+3=4 1+3+5=9 1+3+5+7=16 1+3+5+7+9=25... (answered by solver91311)