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3 years ago

Find the 8th Term for the Geometric Sequence for which a1 - 3 and r = -2

Mathematics

1 answer:

Firdavs [7]3 years ago

4 0

Answer:

-384

Step-by-step explanation:

geometric sequence : every new element is generated by multiplying the previous element always with the same number r.

a(n) = a(n-1) * r

a(n) = a(1) * r^(n-1)

so, a(1) = 3, r = -2

a(8) = ?

a(8) = a(1) * r^7 = 3 * (-2)^7

a negative number to an uneven power is again a negative number.

so, (-2)^7 = -128

3 * -128 = -384 = a(8)

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Hey there!

Before we get to know an Integer and Rational Number, we have to know the Real Number system first.

1. What is Real Number System?

Real Number System is very commonly used in mathematics. It is a number system that is "logical", at least when it comes to solving an equation.

But do you know that the Real Number system can be broken into two categorizes? And what are them?

Real Numbers can be broken into these main two categorizes which are:

Irrational Number
Rational Number

These numbers can also be broken into other categorizes as well! Crazy, ain't it? Well that's how maths work!

Anyways, we will skip Irrational Number since it is off-topic and not related to your question. We will talk about Rational Number instead.

2. What is Rational Number?

Rational Number is a number that can be written in fraction form. That is a simple explanation for the Rational Number. Please lecture or note that approximations aren't considered as rational numbers. Even though π ≈ 22/7 which is in fraction form but it is just an approximation which is considered as Irrational Number. Also if infinity/endless decimal can be written in fraction form as well, they are considered as Rational Number too!

Now we know the meaning of Rational Number. But like I said, the Rational Number can be broken into other categorizes which are:

Integers - Whole number or number without fraction or decimal.
Fractions and Decimals that can be written in fraction form.

And Integers can also be broken into:

Negative Integers
Zero
Positive Integers

3. Conclusion and Answer

Since Integers are subset of Rational Number, we can conclude that Integers are Rational Number.

Hope this helps, and let me know if you have any doubts regarding Real Number system.

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