Question

Find the sum of the arithmetic series -1 + 2 + 5 + 8 + ... where n=7.

Answer 1

We have:

`a_1=\boxed{-1}\\\\n=\boxed{7}\\\\d=a_2-a_1=2-(-1)=2+1=\boxed{3}`

so:

`S_n=(2a_1+(n-1)d)/(2)\cdot n\\\\\\S_7=(2\cdot(-1)+(7-1)\cdot3)/(2)\cdot 7=(-2+6\cdot3)/(2)\cdot7=(-2+18)/(2)\cdot7=(16)/(2)\cdot7=\\\\\\=8\cdot7=\boxed{56}`