Find the value of a4 for this geometric series (i’ll add you on discord if you solve my guy and guyetts)

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

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

college