Question

Please help!! Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66

Answer 1

$r=-4-(-9)=-4+9=5 \\ \\ a_{1}=-9 \\ \\ a_{n}=66 \\ \\ a_{n}=a_{1}+(n-1)r \\ \\ -9+5(n-1)=66 \\ \\ -9+5n-5=66 \\ \\ 5n-14=66 \\ \\ 5n=80 \\ \\ n=16 \\ \\ S_{n}= \frac{a_{1}+a_{n}}{2} *n \\ \\ S_{n}= \frac{-9+66}{2}*16=57*8=456$