Answer
Arithmetic
Sum: $1375$
Work Step by Step
We are given the sequence:
$\{n+2\}$
Compute the difference between two consecutive terms:
$(k+2)-((k-1)+2)=(k+2)-(k+1)=1$
As the difference between any consecutive terms is constant, the sequence is ARITHMETIC. Determine its first element and common difference:
$a_1=1+2=3$
$d=1$
Compute the sum of the first 50 terms:
$S_n=\dfrac{n(2a_1+(n-1)d)}{2}$
$S_{50}=\dfrac{50(2(3)+(50-1)(1)}{2}=1375$
