Answer to Question #42502 in Calculus for shasha

Question

Find the sum of the arithmetic sequence.

17, 19, 21, 23, ..., 35

260

179

37

160

show work and explanation please

Answer 1

We need to find a_1+a_2+...a_n, where a_1=17, a_2=19 and a_n=35.

As we know a_n=a_1+(n-1)*d. In our case d=2 (a_2-a_1=2).

a_1+a_2+...+a_n=a_1+a_1+d+a_1+2d+...+a_1+9d=10a_1+(1+2+3+...+9)*d=10*a_1+(9(9+1)/2)*d=10*17+90=260.