What is the explicit formula for this geometric sequence? 8, 4 2, 1

Mathematics

1 answer:

11Alexandr11 [23.1K]4 years ago

3 0

Answer:

Step-by-step explanation:

The standard form for the explicit formula of a geometric sequence is given by:

$a_n=a\cdot(r)^{n-1}$

Where a is the initial term, r is the common ratio, and n is the nth term.

Our sequence is: 8, 4, 2, 1...

So, we can see that our initial term or a is 8.

Each subsequent term is half of the previous one. So, our common ratio is 1/2.

Let's substitute 8 for a and 1/2 for r to acquire:

$a_n=8\cdot(\frac{1}{2})^{n-1}$

So, our answer is C.

And we're done!

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See below:

Step-by-step explanation:

So, the first step to solving the problem is to find out what type of triangle it is

and what rule of goemetry we can use to solve it.

Finding What Theorem We Can Use

So, the first step is to figure out what theorem we can use to solve the problem and how they can help us. By looking at it, we can see that it is an Isosceles Triangle due to the two sides being equal and 1 side not being equal.

One Theorem used on the Isosceles Triangle is the Base Angles Theorem. This states that the bottom two angles of the sides on the Isosceles triangle are equal to each other. So in this case if we letter the triangle A on the top, B as the Left, and C as the right. It would say this: