Question

What conjecture can you make about the sum of the first 35 positive even numbers?

Answer 1

Do you have to find the sum of the first 35 positive even numbers?

Answer 2

I have to find 2 numbers that multiply together to equal the sum of the first 35 positive numbers

Answer 3

Ah, I see.

Answer 4

Exercise: Find the sum of the first \(n\) positive even numbers.

Hint: It is an arithmetic progression with first term \(2\), last term \(2n\) and number of terms \(n\).

Answer 5

Thank you

Answer 6

Did you figure it out?

Answer 7

\[2+4 + 6 +\cdots + 70=\\
2(1+2+3+ +\cdots +35)=\\
\]

Answer 8

Apply the formula
\[1+2+3+\cdots+n=\frac{n(n+1)}2
\]

Answer 9

\[1+2+3+\cdots +35=\frac {35\times 36}2\]

Answer 10

\[2(1+2+3+\cdots+ 35)= 35\times 36
\]