# Math Help - arithmetic progression--ans to confirm

1. ## arithmetic progression--ans to confirm

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

2. Originally Posted by nikk
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 $a_n=2(n+1)+1=2n+3$

So we must solve $\sum_{n=1}^{k}\left\{2n+3\right\}=357$

Using the fact that $\sum_{n=1}^{k} c=ck$ and $\sum_{n=1}^{k}n=\frac{k(k+1)}{2}$ we must solve $2\cdot\frac{k(k+1)}{2}+3k=357$. Solving indeed shows that the only pertinent answer is $k=17$

Good job!