Series question with unknown limit I am doing an A Level Core 2 paper and the last question caught me out. The question is:
$$\sum_1^{2N} (3r+5) - \sum_1^N (3r+5) = 1256$$
Find N.

How can I do this? I've worked out so far that the LHS can be written as $\sum_N^{2N} 3r+5$ but I can't figure out where to go from there. How do I find N? 

As $3(n+1)+5-[3n+5]=3$ which is the common difference, 
We need $\sum_{n=N+1}^{2N}(3n+5)$
Now $\sum_{r=c}^d[a+rD]=\dfrac{d-c+1}2\left[2\{a+cD\}+(d-c)D\right]$
