All categories

3 years ago

Find an explicit formula for the following sequence, an which starts with a1=−1. −1,1/2,−1/3,1/4,−1/5,…

Mathematics

1 answer:

Dimas [21]3 years ago

5 0

Answer:

The sequence can be represented by the formula of its nth term:

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

Step-by-step explanation:

Notice that we are in the presence of an alternate sequence (the values alternate from negative to positive. Therefore we need to take into account that there should be a factor "-1" raised to the "n" value for the sequence. Also, given that the sequence looks in absolute value like the harmonic sequence, we conclude upon the following general form for the "nth" term of the sequence:

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

You might be interested in

A trail is 2940 miles long. it begins in city a and ends in city

d1i1m1o1n [39]

In this question, the trail is 2940 miles long and Manfred is already hiking the 3/7 of the trail. You are asked how many miles he has a hike. Then to find it you just need to multiply the trail length with the ratio of hike/total trail. The calculation would be:

2940 miles * 3/7 = 1260 miles

5 0

4 years ago

How many more sides does a nonagon have than a pentagon?

lana [24]

Answer:4

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

What is the answer to this problem? Ignore the work. What is the correct answer?

yan [13]

Answer:

c = 42.5

Step-by-step explanation:

The legs of the triangle are a and b and the hypotenuse is c

Let a be the shorter leg

The hypotenuse is 5 more than the longest leg

c = b+5

The shortest leg is 20

a = 20

We can use the Pythagorean theorem

a^2 +b^2 = c^2

Substituting in what we know from above

20 ^2 + b^2 = (b+5)^2

FOIL (b+5)^2 = b^2 +5b+5b +25 = b^2+10b+25

400 + b^2 = b^2+10b+25

Subtract b^2 from both sides

400+b&2-b^2 = b^2 -b^2 +10b+25

400 = 10b+25

Subtract 25 from both sides

400-25 = 10b+25-25

375 = 10b

Divide by 10

375/10 = 10b/10

37.5 = b

But we want to find c

c=b+5

c = 37.5+5

c = 42.5

6 0

3 years ago

61 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. T

Molodets [167]

Complete question :

61 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows:

Pairs of Shoes4__5__6__7 __8 __9 __10 __11

Frequency : _ 8 _ 8 __5 _ 5 _ 9 __11 __7 ___8

Answer:

Mean = 7.64 ;

Median = 8

Q1 = 5

Q3 = 9

Atleast 10 pairs = 24.6

76% is equivalent to

Step-by-step explanation:

Round all your answers to 4 decimal places where possible.

The mean is:

Σfx /Σf

((8*4)+(5*8)+(6*5)+(7*5)+(8*9)+(9*11)+(10*7)+11*8)) ÷ (8+8+5+5+9+11+7+8) = 7.64

The median is:

0.5(n+1)th observation

n = frequency = 61

0.5(61 +1) = 1/2 * 62 = 31st observation

= 8

First quartile:

0.25(n+1)th observation

n = frequency = 61

0.25(61 +1) = 1/4 * 62 = 15.5

(15 + 16)th observation ÷ 2 = (5 + 5) / 2 = 5

The sample standard deviation is:

The third quartile is:

0.75(n+1)th observation

n = frequency = 61

0.75(61 +1) = 1/4 * 62 = 46.5

(46 + 47)th observation ÷ 2 = (5 + 5) / 2 = 9

What percent of the respondents have at least 10 pairs of Shoes? %

(7 + 8) / 61 = 15 / 61 = 0.246

76% of all respondents have fewer than how many pairs of Shoes?

(76 / 100) * 61

0.76 * 61

= 46.36

(46th + 47th)

(9 + 10) = 19 /2 = 9.5 = 10

6 0

3 years ago

Math Please help!<br><br> x^2 + 36x + 103 <br><br> What is the value of A, B, and C?

Akimi4 [234]

Go from left to right

a= x^2

b= 36x

c= 103

6 0

3 years ago