All categories

3 years ago

Write an explicit formula for a^n the nth term of the sequence 1,3,9....

Mathematics

1 answer:

frutty [35]3 years ago

7 0

Answer:

a_n = 3^(n -1)

Step-by-step explanation:

The n-th term of a geometric sequence with first term a1 and common ratio r is given by ...

a_n = a1·r^(n-1)

Your sequence has first term 1 and ratio r=3, so the sequence is given by ...

a_n = 3^(n -1)

_____

Comment on sequences and series

The sequences we commonly study are "arithmetic" and "geometric." Each of these has an explicit formula for the n-th term, based on the first term and the common difference or ratio. Similarly, each series (sum of terms of a sequence) also has a formula. That's 4 formulas to keep track of; not difficult. One of them, the formula for the n-th term of a geometric sequence, is shown above.

You might be interested in

You are standing 6 feet away from the stage and your friend is standing 7 feet away from the stage. You are standing on a platfo

coldgirl [10]

Answer:

The distance from your eyes to the stage is 8.85 ft

Step-by-step explanation:

Your distance to the stage is 6 feet

Your eyes are 6.5 feet tall

You need to find the distance of your eyes towards the stage.

This situation can be modeled using a rectangle triangle, where the adjacent side x is the horizontal distance to the stage and the opposite side h is the vertical distance of your eyes to the stage.

Observe the attached image.

Then, we look for the distance z from your eyes to the stage. This distance is the hypotenuse of the right triangle.

So, using the Pythagorean theorem we have:

$z ^ 2 = h ^ 2 + x ^ 2\\\\z = \sqrt{h^2 +x^2}$

Where

$h = 6.5\ ft\\\\x = 6\ ft$

therefore:

$z = \sqrt{(6.5)^2 +(6)^2}\\\\z =8.85\ ft$

4 0

3 years ago

What are the next three terms of the geometric sequence 32, -16, 8, …?

Marrrta [24]

Answer:

B is your answeer

Step-by-step explanation:

GL hope i helped<333!!

7 0

3 years ago

A boat is marked up 20% on the original price the original price was $50 what is the sale price of the boat before sales taxes

bezimeni [28]

Answer:

42.9

Step-by-step explanation:

20% of 50 is 10

so its 40

40 + taxes

40 + (40*.0725)

6 0

3 years ago

(a^(2)-4ac+3bc)/(a^(2)-ab+bc-ac)+(a+3b)/(b-a)+(a+2c)/(a-c)

Bingel [31]

Answer:

The answer is −a^4 + 5a^3b + 2a^3c − 4a^2b^2 − 10a^2bc − a^2c^2 + 8ab^2c + 5abc^2 − 4b^2c^2 / −a^4 + 2a^3b + 2a^3c − a^2b^2 − 4a^2bc − a^2c^2 + 2ab^2c + 2abc^2 − b^2c^2

Step-by-step explanation:

This the equation being simplified

4 0

3 years ago

Read 2 more answers

What the simplified form of x- 1 +4+7x-3

Nuetrik [128]

Collect like terms (x + 7x) + (-1 + 4 - 3)

Simplify

Answer: 8x

7 0

3 years ago