Find the 14th term of the following geometric sequence. 4, 8, 16, 32, ...

Mathematics

2 answers:

Softa [21]3 years ago

8 0

Answer:

32768

Step-by-step explanation:

$an = (a1)(r^{n-1} )\\\\$

where an stands for the number in the series,

a1 is the first number in the series

and n is the number or the order in which the number in the series we are looking at. r is the ratio.

in this we case we are looking for the 14th number, where n = 14, the first number is 4 and r is the ratio they increase by a factor of 2. so r = 2.

Substituting all of these back into the equations would give us:

This will give us the answer.

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xz_007 [3.2K]3 years ago

4 0

Answer:

65536

Step-by-step explanation:

multiply each term by 2 until you get to the 14th term. the 14th term is 65536

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A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$