# ALGEBRA

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(a) What is the sum of the first 60 consecutive odd numbers?
Tell whether it illustrates inductive or deductive reasoning.
inductive reasoning deductive reasoning

(b) What is the sum of the first 1,200 consecutive odd numbers?
Tell whether it illustrates inductive or deductive reasoning.
inductive reasoning deductive reasoning

• ALGEBRA -

a)
Sum(1 odd numbers) = 1
sum(first 2 odd numbers) = 1+3=4
sum(first 3 odd numbers) = 1+3+5 = 9
mmmhhh?
they look like perfect squares

sum(first 4 odd numbers) = 1+3+5+7 = 16
appears that sum(n odd numbers) = n^2
so Sum(first 60 odd numbers) = 60^2 = 3600

test it with an arithmetic sequence method
1+3+5+7 + ... 60 = ?
a = 1, d=2, n=60
sum(60) = (60/2)(2 + 59(2)) = 3600

ok, then!!!

According to your text or course notes, what kind of reasoning did I just use?

b) sum(1200) = 1200^2 = ....

• ALGEBRA -

-38= 2 (n-1)

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