Answer
$3570$
Work Step by Step
Recall the formulas:
$\displaystyle \sum_{k=1}^{n} (ca_k)=c \ \sum_{k=1}^{n} a_k$
and
$ \displaystyle \sum_{k=1}^{n} k=\dfrac{n(n+1)}{2}$
We can see that for the given sequence, the index does not start at 1. So, we will re-write the given sequence as:
$\sum_{k=10}^{60} (2k)=$ (Terms from 10 to 60) = (Terms from 1 to 60) - (Terms from 1 to 9)
We rewrite the sequence as stated above and apply the sum formulas:
$\displaystyle \sum_{k=10}^{60} (2k)= \sum_{k=1}^{60} (2k) -\sum_{k=1}^{9} (2k) \\= (2) \sum_{k=1}^{60} k - (2) \sum_{k=1}^{9} k \\= 2 [ \displaystyle \dfrac{60(60+1)}{2} -\dfrac{9(9+1)}{2}] \\=2 (1830 -45) \\= 3570$
