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 70 of this series?  Answers
A) 6845 B) 7225 C) 7665 D) 8025 E) 8485
Each term of the series has the form (n+n+1+n+2) = 3n+3   Since the series goes from 1 to 70, the sum of the series is:   3(1+2+...+70) + 70(3) ( + +1+ +2)= 
<gadget id="calculator">( + +1+ +2)</gadget>
<output>3</output>
3n+3   Since the series goes from 1 to 70, the sum of the series is:   3(1+2+...+70) + 70(3)=   3(70)(71)/2 + 70(3) =   105*71 + 210= 
<gadget id="calculator">105*71 + 210</gadget>
<output>7_665</output>
7665   The answer is 7665.
<result>C</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 70 of this series?