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Stuck on geometric series question (in picture)

Stuck on geometric series question (in picture)-example-1

1 Answer

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Answer:

The value of a7 is 128

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

User Beniamin Szabo
by
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