Question

Use sigma notation to represent the following series for the first 10 terms. 3+ (-6) +12+(-24)

Answer 1

Answer: - 1023

Step-by-step explanation:

Given

Sequence is $3+(-6)+12+(-24)...$

The following sequence is a geometric series with common ratio $r=-2$

first term $a=3$

$Sum=\sum _{i=1}^{n}ar^{n-1}=\dfrac{a(1-r^n)}{1-r}$

$Sum=\sum _{i=1}^{n}3(-2)^{n-1}=\dfrac{3(1-(2)^10)}{1+2}$

$Sum=\sum _{i=1}^{n}3(-2)^{n-1}=-1023$