Question

What is the sum of the arithmetic sequence 8, 14, 20 …, if there are 24 terms?

Answer 1

Each term is six more than the previous, thus, the series can be represented as follows:\[(8+6*0)+(8+6*1)+(8+6*2)+...+(8+6*23)\]This is equivalent to\[8*24+(0+1+2+...+23)*6\]The summation in the parenthesis can be reduced as follows, recognizing that the sum of each symmetrically placed number pair equals 23 (i.e. - 23+0=22+1=21+2, etc., for a total of twelve pairs since there are twenty-four terms)\[8*4+(12*23)*6\]Which is equal to\[1688\]