Question

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

Answer 1

Answer:

yes it is the 10th term in the series

Step-by-step 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 = $\frac{a_{2} }{a_{1} }$ = $\frac{14}{7}$ = 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