Question

The first term of an arithmetic sequence is 2 and the fourth term is 11. Find the sum of the first 50 terms.

Answer 1

$a_1=2;\ a_4=11;\ S_{50}=?\\\\a_4-a_1=3d\\\\subtitute\\\\3d=11-2\\3d=9\ \ \ |divide\ both\ sides\ by\ 3\\d=3\\\\S_n=\dfrac{[2a_1+(n-1)d]\cdot n}{2}\\\\subtitute\\\\S_{50}=\dfrac{(2\cdot2+(50-1)\cdot3)\cdot50}{2}=(4+49\cdot3)\cdot25=(4+147)\cdot25\\\\=151\cdot25=3,775\\\\Answer:\boxed{S_{50}=3,775}$