Question

Is 3584 a term of the series 7+14+28+56........?

(please answer if you know; this is the question from geometric series:- General progression)
(full steps and process required)
(No spam answers or else you'll be reported )​

Answer 1

yes it is the 10th term in the series

Explanation:

The nth term of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 7 and r =
`(a_(2) )/(a_(1) )` =
`(14)/(7)` = 2 , then

`a_(n)` = 7
`(2)^(n-1)`

Equate
`a_(n)` to 3584 and solve for n

7
`(2)^(n-1)` = 3584 ( divide both sides by 7 )

`2^(n-1)` = 512 , that is

`2^(n-1)` =
`2^(9)`

Since the bases on both sides are equal, both 2 , then equate the exponents

n - 1 = 9 ( add 1 to both sides )

n = 10

3584 is the 10th term in the series