Confused!!!!!

[Maryanne]

I have been practising how to find the sum of a series only problem is I'm not sure how to figure it out when brackets and unknown variables are thrown in.

My question is:

Find the sum of the series; (x+y)+(x+2y)+.......+(x+10y)


I fgiure it's an arithmetic series so I could use

sn= n/2(2a+(n-1)d)

but i'm not sure how to handle the X and y's!

 

[pka]

I do not want to confuse you.
However I have found this form of the sum to be more understandable:
\(\displaystyle S_n = na + \frac{{\left( {n - 1} \right)n}}{2}d\).

In the above a is the first term of the sequence.
In any case, for your problem, a=x+y , d=y and n=10.

 

[Maryanne]

actually the rearranging of the formula is less confusing thanks pka

so i substiuted everything into the new formula;


Sn= 10(x+y)+(10-1)(10)/2 (y)

=10x+10y+ (90/2)(y)

=10x+10y+45y

Therefore the sum of this equation is 10x+55y

am i right????

 

[pka]

WAY TO GO! Full marks.