-10+(-5)+0+5+10+... a.)n=19 b.)Sn=375 for part (a) find the sum of the first n terms of the arithmetic series. For part (b) find n for the given sum Sn

Question

a.)n=19 b.)Sn=375 for part (a) find the sum of the first n terms of the arithmetic series. For part (b) find n for the given sum Sn

Answer 1

-10 + (-5) + 5...+n

= -10 + (-10+5*1) + (-10+5*2) + (-10 + 5*3)....(-10+5*(n-1))

= -10*n + 5*(n-1)*n/2

For n = 19, =-10*19 + 5*18*19/2 = 665.  

For Sn = 375, solve for n to get n = 15.