Hello everyone, how are you today, hope you had an amazing Halloween!

I have this question i dont understand , i have looked up many websites but i dont understand their answers.

i would be grateful if any of you would explain it to me in detail.

If there are (2n+1) terms in an arithmetic series, prove that the ratio of the sum of odd place terms to the sum of even place terms is (n+1) : n .

rosala Nov 4, 2017

#1**+2 **

Mmmmm....I'll try rosala ....!!!

Let's suppose that we have a partial series like this where a = the first term and d is the common difference between terms

a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) + (a + 5d) + (a + 6d) + (a + 7d) + (a + 8d)

Let n be the number of even place terms

And n + 1 the number of odd place terms

Then the sum of the even place terms is :

n *a + n^2* d = n (a + n*d)

And the sum of the odd place terms is :

(n + 1) * a + ( n+1) (n)* d = (n + 1) (a + n*d) for n ≥ 0

So....the ratio of the sum of the odd place terms to the even place terms is :

(n + 1) (a + n*d) ( n + 1)

_____________ = _______

n (a + n*d) n

CPhill Nov 4, 2017