Stuck on geometric series question (in picture)

The value of a7 is 128

Step-by-step explanation:

* Lets revise the rule of the geometric series

-There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)  

* General term (nth term) of a Geometric series:

# a1 = a  ,  a2  = ar  ,  a3  = ar2  ,  a4 = ar3  ,  a5 = ar4

# an = ar^n-1, where a is the first term , r is the constant ratio

   between each two consecutive terms , and n is the position

   of the term in the series

* Now lets solve the problem

∵ a = 2

∵ r = -2

* To find a7 put n = 7

∵ an = a (r)^n - 1

∴ a7 = 2 (-2)^(7 - 1) = 2 (-2)^6

∵ (-2)^6 = 64 ⇒ even power canceled the negative sign

∴ a7 = 2 (64) = 128

∴ The series is : 2 , -4 , 8 , -16 , 32 , -64 , 128 ,

* The value of a7 is 128

do have an equation or graph or

step-by-step explanation:

faster, im not sure why but i know it is faster