Question

Find the sum of the sequence 36 37 38 39 ... 109=

Answer 1

It's an arithmetic sequence:

$a_1=36;\ a_2=37;\ a_3=38;\ ...\ ;\ a_{74}=109\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\a_1=36;\ n=74;\ a_{74}=109\\\\S_{74}=\dfrac{36+109}{2}\cdot74=\dfrac{145}{2}\cdot74=72.5\cdot74=5365$