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3 years ago

Indicate a general rule for the nth term of this sequence. 6a, 3a, 0, -3a, -6a, . . .

Mathematics

2 answers:

Lesechka [4]3 years ago

8 0

6a-(n-1)(3a) is the nth term
Expanding we get 6a-3an+3a=9a-3an=3a(3-n)
SOLUTION: nth term is 3a(3-n)

Elza [17]3 years ago

4 0

Answer:

The answer is $a_n=6a-3a(n-1)$

Step-by-step explanation:

In order to determine the general rule, we have to identify the difference between each term. We have to subtract every two continuous terms:

$3a-6a=-3a\\0-3a=-3a\\-3a-0=-3a\\-6a-(-3a)=-6a+3a=-3a$

Then, we know that we have to subtract -3a to every next term. The first term of the sequence is 6a and after that we have to subtract -3a since the second to the nth term.

Thus the nth term of the sequence is:

$a_n=6a-3a(n-1)$

To check the expression:

$n=1\\a_1=6a-3a(1-1)=6a-3a(0)=6a\\\\n=3\\a_3=6a-3a(3-1)=6a-3a(2)=6a-6a=0$

So, the expression is right.

You might be interested in

The weights of certain machine components are normally distributed with a mean of 8.04 g and a standard deviation of 0.08 g. Fin

NISA [10]

Answer:

The bottom 3 is separated by weight 7.8896 g and the top 3 is separated by weight 8.1904 g.

Step-by-step explanation:

We are given that

Mean, $\mu=8.04 g$

Standard deviation, $\sigma=0.08g$

We have to find the two weights that separate the top 3% and the bottom 3%.

Let x be the weight of machine components

$P(Xx_2)=0.03$

$P(X$

=0.03

From z- table we get

$P(Z1.88)=0.03$

Therefore, we get

$\frac{x_1-8.04}{0.08}=-1.88$

$x_1-8.04=-1.88\times 0.08$

$x_1=-1.88\times 0.08+8.04$

$x_1=7.8896$

$\frac{x_2-8.04}{0.08}=1.88$

$x_2=1.88\times 0.08+8.04$

$x_2=8.1904$

Hence, the bottom 3 is separated by weight 7.8896 g and the top 3 is separated by weight 8.1904 g.

5 0

2 years ago

A city has a population of 230,000 people. Suppose that each year the population grows by 8.5%. What will the population be afte

worty [1.4K]

Answer:

720,682.92

Step-by-step explanation:

8.5% = 0.085

P(t) = Initial Population * (1 + rate)t

P(t) = 230,000(1 + 0.085)t

P(t) = 230,000(1.085)t

P(14) = 230,000(1.085)14

P(14) = 720,682.82

6 0

2 years ago

Which of the following are roots of the polynomial function? Check all that apply.

lutik1710 [3]

You know 1 is not a root because the sum of the coeffcients of the equation is 14, not zero.

It is fairly easy to try 3 by synthetic division (see attachment), which tells you that 3 is a root and the remaining quadratic factor is x²-3x-5. The quadratic formula tells you the roots of that factor are

... x = (-b±√(b²-4ac))/(2a) = (3±√29)/2

The appropriate choices are

... C. (3-√29)/2

... D. (3+√29)/2

... F. 3

_____

The quadratic formula tells you the solution to

... ax²+bx+c=0

is x = (-b±√(b²-4ac))/(2a)

We have a=1, b=-3, c=-5.

8 0

2 years ago

Strontium-90 has a half-life of about 29 years. After 65 years, about how many grams of a 25-gram sample will remain?

konstantin123 [22]

Answer:

Ending Amount = Beginning Amount / 2 ^ n

where 'n' = number of half-lives n = 65 / 29 = 2.2413793103

Ending Amount = 25 g / 2^2.2413793103

Ending Amount = 25 / 4.7284892286

Ending Amount = 5.2871009727 g = 5.29 g (rounded)

Step-by-step explanation:

3 0

3 years ago

What does the f(n - 1) represent?

leonid [27]

I'm assuming that you are talking about sequences <3

In the context of a recursive formula where we have "n-1" in sub-index of "a", you can think of "a" as the previous term in the sequence. In the context of an explicit formula like "-5+2(n-1)" "n-1" represents how many times we need to add 2 to the first term to get the nth term.

Dw if you don't understand, sequences and functions isn't an easy topic

3 0

2 years ago