All categories

3 years ago

Write the nth term of the following sequence in terms of the first term of the sequence.

Mathematics

1 answer:

vovikov84 [41]3 years ago

6 0

Givens

Sequence 2, - 4, 8, -16, 32 ....

First term = a = 2

Problem

Find the nth term

tn = (-1 )^(n -1) * (a)^n answer or

tn = (-1)^(n - 1) * 2^n

where a is defined as the first term (it usually is given that designation).

Try a few to make sure the formula is correct

n = 1

t1 = (-1)^(1 - 1) * 2^1

t1 = (-1)^0 * 2

t1 = 1 * 2 = 2

n =2

t2 = (-1)^(2 - 1) * 2^2 = (-1)^1 * 4 = -4

You might be interested in

Solve for x. –4.5(x – 8.9) = 12.6 OVEC Enter your answer, as a decimal, in the box.

Gnoma [55]

Step-by-step explanation:

just take -4.5 the right side

3 0

3 years ago

Marty and Ethan both wrote a function, but in different ways.

marishachu [46]

Question:

Marty and Ethan both wrote a function, but in different ways.

Marty

y+3=1/3(x+9)

Ethan

x y

-4 9.2

-2 9.6

0 10

2 10.4

Whose function has the larger slope?

1. Marty’s with a slope of 2/3

2. Ethan’s with a slope of 2/5

3. Marty’s with a slope of 1/3

4. Ethan’s with a slope of 1/5

Answer:

Marty’s with a slope of 1/3 has the larger slope

Solution:

Given that Marty equation is:

$y + 3 = \frac{1}{3}(x+9)$

The point slope form is given as:

$y - y_1 = m(x-x_1)$

Where, "m" is the slope of line

On comapring both equations,

$m = \frac{1}{3}$

Ethan wrote a function:

Consider any two values from the table we have;

(0, 10) and (2, 10.4)

The slope is given by formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

From above two points,

$(x_1, y_1) = (0, 10)\\\\(x_2, y_2) = (2, 10.4)$

Therefore,

$m = \frac{10.4-10}{2-0}\\\\m = \frac{0.4}{2} \\\\m = 0.2$

Thus we get,

$\text{Slope of Ethan} < \text{Slope of Marty}$

Therefore, Marty’s with a slope of 1/3 has the larger slope

4 0

3 years ago

Read 2 more answers

If a hiker starts at sea level and increases her elevation at a rate of 1 foot per minute what will her elevation be in 20 minut

sattari [20]

Answer:

20 feet above sea level.

Explanation:

This can be solved by looking at the Rate of Change. It is given that for ONE minute that passes by, her elevation increases by ONE foot.

With this rate, after 20 minutes, the elevation can be shown as:

20 min × 1 foot= 20 feet.

4 0

3 years ago

Read 2 more answers

Write a vector equation of the line that passes through P(4, 7) and is parallel to a = (3, 8).

Anvisha [2.4K]

Answer:

Step-by-step explanation:

(x,y) = P + (a)t

(x,y) = (4,7) + t(3,8)

(x,y) - (4,7) = t(3,8)

(x-4, y-7) = t(3,8)

4 0

3 years ago

Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.

Aleks [24]

Answer:

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

Step-by-step explanation:

The actual Series is::

$\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$

The method we are going to use is comparison method:

According to comparison method, we have:

$\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n$

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

$=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}$

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}$

Now:

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}$