Answer
$3850$
Work Step by Step
The sum of the first $n$ terms of an arithmetic sequence can be obtained by the following formula: $\frac{n(a_1+a_n)}{2},$ where $a_1$ is the first term, $a_n$ is the nth term and $n$ is the number of terms.
The nth term of an arithmetic sequence can be obtained by the following formula: $a_n=a_1+(n-1)d$, where $a_1$ is the first term and $d$ is the common difference.
Hence here: $d=4,n=50,a_1=4\cdot1-25=4-25=-21,a_{50}=4\cdot50-25=200-25=175$
Thus the sum:$\frac{50(-21+175)}{2}=25\cdot154=3850$
