Given :
sequence of 5,7,9,11....
Find :
how many consecutive terms need to be added to obtain 357?
My ans:
n = 17 or -21(ignore)
so n = 17
tq for your time on it
So $\displaystyle a_n=2(n+1)+1=2n+3$
So we must solve $\displaystyle \sum_{n=1}^{k}\left\{2n+3\right\}=357$
Using the fact that $\displaystyle \sum_{n=1}^{k} c=ck$ and $\displaystyle \sum_{n=1}^{k}n=\frac{k(k+1)}{2}$ we must solve $\displaystyle 2\cdot\frac{k(k+1)}{2}+3k=357$. Solving indeed shows that the only pertinent answer is $\displaystyle k=17$
Good job!