Answer:
The value of a4 is 6
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 number in the series
* Now lets solve the problem
- The rule of the series is 2/9 (3)^n - 1
∴ a = 2/9 and r = 3
- To find a4 put n = 4
∴ a4 = 2/9 (3)^(4 - 1) = 2/9 (3)³ = 2/9 (27) = 6
∴ The series is 2/9 , 2/3 , 2 , 6 , ........
* The value of a4 is 6
