Question

Given d= 5, S9= 75, find a and an

Answer 1

$S_9=\frac{9}{2}[2a+(9-1)d]\\\\ S_9=\frac{9}{2}[2a+40]\\\\ S_9=9[a+20]\\\\\frac{75}{9}=a+20\\\\ a+20=\frac{75}{9}\\ \\a=-\frac{35}{3}$

$a_9=\frac{-35}{3}+(9-1)5\\ \\a_9=\frac{-35}{3}+40\\ \\a_9=\frac{95}{3}$