Answer
Arithmetic
Sum: $\dfrac{n(n+11)}{2}$
Work Step by Step
We are given the sequence:
$a_n=\{n+5\}$
Determine the difference between two consecutive terms:
$a_{k+1}-a_k=((k+1)+5)-(k+5)=k+6-k-5=1$
As the difference between consecutive terms is constant, the sequence is arithmetic.
Its elements are:
$a_1=1+5=6$
$d=1$
Compute the sum $S_n$ of its first $n$ terms:
$S_n=\dfrac{n(2a_1+(n-1)d)}{2}=\dfrac{n(2(6)+(n-1)(1))}{2}=\dfrac{n(12+n-1)}{2}=\dfrac{n(n+11)}{2}$
