MathRevolution wrote:

If the sum of all the even numbers from 1 to n(n: odd number) is 69*70, what is the value of n?

A. 135

B. 137

C. 139

D. 141

E. 143

1. If you don't remember the formula for summing consecutive even integers, you can use the general formula for the sum of any evenly spaced set where

Sum =

average (arithmetic mean) *

number of termsThe average (arithmetic mean) of evenly spaced consecutive numbers is First + Last divided by 2.

2. Given 69*70, from the basic formula you know that:

--

one of those numbers is the average of the first and last terms, and

--

the other number is the

number of termsThe first even number from 1 to n (where n is odd) is 2.

Looking again at 69*70 . . . the average of two even terms (first and last)

cannot be odd.

So 69 must be the number of terms.

And

70 must be the average of 2 and the last even term.

3. \(\frac{2 + Last Even}{2}\)= 70

2 + last even term = 140

Last even term = 138.

n is odd.

For 138 to be

included in 1 to n . . . n must be 139. (Or, from the outset it should be clear that the last even term is n - 1.)

Answer C

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