Answer
Arithmetic
Sum: $2300$
Work Step by Step
We are given the sequence:
$\{2n-5\}$
Compute the difference between two consecutive terms:
$(2(k+1)-5)-(2k-5)=2k+2-5-2k+5=2$
As the difference between any consecutive terms is constant, the sequence is ARITHMETIC. Determine its first element and common difference:
$a_1=2(1)-5=-3$
$d=2$
Compute the sum of the first 50 terms:
$S_n=\dfrac{n(2a_1+(n-1)d)}{2}$
$S_{50}=\dfrac{50(2(-3)+(50-1)(2))}{2}=2300$
