For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 50 of this series? Select:
A) 3975
B) 4125
C) 4375
D) 4525
E) 4775
Each term of the series has the form (n+n+1+n+2) = 3n+3   Since the series goes from 1 to 50, the sum of the series is:   3(1+2+...+50) + 50(3) ( + +1+ +2)= 
<gadget id="calculator">( + +1+ +2)</gadget>
<output>3</output>
3n+3   Since the series goes from 1 to 50, the sum of the series is:   3(1+2+...+50) + 50(3)=   3(50)(51)/2 + 50(3) =   75*51 + 150= 
<gadget id="calculator">75*51 + 150</gadget>
<output>3_975</output>
3975   The answer is 3975.
<result>A</result>
For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 50 of this series?