Friday

August 29, 2014

August 29, 2014

Posted by **Riana** on Tuesday, January 1, 2013 at 4:47pm.

how to find the sum of it.

- math -
**Knights**, Tuesday, January 1, 2013 at 4:53pmHi, first thing you do is to want to find Formulas formulas formulas. hey, this is a arithmetic sequence!

An arithmetic sequence is A series such as 3 + 7 + 11 + 15 + ··· + 99 or 10 + 20 + 30 + ··· + 1000 which has a constant difference between terms. The first term is a1, the common difference is d, and the number of terms is n. The sum of an arithmetic series is found by multiplying the number of terms times the average of the first and last terms.

The sum of an arithmetic sequence is a_1+a_n/2 *n

All you need to know is that the sum is the first term plus the last term divided by 2 times the number of terms is the sum.

so...1+100 = 101. 101/2 * number of terms is the answer.

one more thing...the way to find how many numbers in a sequence which goes up by increments of 1 is minus the first from last and +1.

thus we have 100-1 = 99. 99+1= 100

so 101 /2 * 100 = 50 * 101 = 5050

- math -
**Reiny**, Tuesday, January 1, 2013 at 7:40pmThere is the old story about the famous mathematician Gauss being given this question along with the rest of the class as "busy work" back in grade school

He thought about it for a while and came up with the answer of 5050

He figured:

the first plus the last = 101

the 2nd plus the 2nd last = 101

the 3rd plus the 3rd last = 101

hey,,,, aren't there just 50 of those sums ?

and he was able to do 50 x 101 = 5050 in his head

**Related Questions**

Precalculus - Find the sum of 20 (summation notation symbol)k=1 then (3k-5) If ...

Math - Minimizing Sum: Find two positive numbers whose sum is 100 and the sum of...

MATH !!!!!!!!! HELP - Find the exact value (either decimal or fraction form) of ...

math - Find the exact value (either decimal or fractional form) of the first ...

Problem Solving Math Question - Find the sum of all the numbers in the following...

sum fun (math) - find a quick and easy method to compute the sum of the first ...

Math - The sum to infinity of a G.P. is 16 and the sum of the first 4terms is 15...

Math - X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of ...

math - If 28% of a sum is $100.80, what is the sum? A. $129.02 B. $277.78 C. $...

Discrete mathematics - I need help solving this problem, I have followed the ...