Question

Find the sum of the first 8 terms of the sequence. Show all work for full credit.

1, -3, -7, -11, ...

Answer 1

1 - 4 = -3. -3 - 4 = -11.

subtract by -4 until you have 8 numbers.

then add al the numbers together.

1+-3+-7+-11+-15+-19+-23+-27 = -104

Answer 2

`1, -3, -7, -11, ...\ \ \ \ \rightarrow\ \ \ the\ arithmetic\ sequence\\\\the\ difference\ of\ the\ sequence\ is\ \ \ \ d=-3-1=-4\\\\the\ sum:\ \ \ \ S_n= \frac{\big{2\cdot a_1+(n-1)\cdot d}}{\big{2}} \cdot n\\\\\\S_8= \frac{\big{2\cdot1+(8-1)\cdot(-4)}}{\big{2}} \cdot8=(2-28)\cdot4=-26\cdot4=-104\\\\Ans.\ The\ sum\ is\ -104.`