Find sum of -3,2,7,12....,132Arithmetic series
\(a_1=-3 \\ d=2-(-3)=5 \\ a_n=132 \\ \\ a_n=a_1+d(n-1) \\ 132=-3+5(n-1) \\ 132=-3+5n-5 \\ 132=-8+5n \\ 140=5n \\ n=28 \\ \\ S_n=\frac{n(a_1+a_n)}{2} \\ S_{28}=\frac{28(-3+132)}{2}=\frac{28 \times129}{2}=14 \times 129=1806\)The sum is 1806.
