1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ehidna [41]
3 years ago
7

The third term in an arithmetic sequence is 14 and the fifth term is 20. If the first term is a1, which is an equation for the n

th term of this sequence?
Mathematics
1 answer:
Kruka [31]3 years ago
5 0

Answer:

The equation for nth term is 3n + 5.

Step-by-step explanation:

Let a1 be a,

a3 = a + (n - 1)d

or, 14 = a + (3 - 1)d

so, 14 = a + 2d

Now,

a5 = a + (n - 1)d

or, 20 = a + (5 - 1)d

or, 20 = a + 4d

now,

a + 4d = 20

a + 2d = 14

now,

a + 4d - ( a + 2d) = 20 - 14

or, a + 4d - a - 2d = 6

or, 2d = 6

so, d = 3

Now,

a + 2d = 14

or, a + 2(3) = 14

or, a = 14 - 6

so, a = 8

Now,

an = a + (n - 1)d

or, an = 8 + (n - 1)3

or, an = 8 + 3n - 3

so, an = 3n + 5

You might be interested in
There are 24 books on the bookcase 3/4 of these books are science fiction how many books are science fiction
jok3333 [9.3K]

Answer:

<u>18 of the books are science fiction.</u>

Step-by-step explanation:

24/4 = 6

Science fiction - 6+6+6 = 18

Not science fiction - 24 - 18 = 6

7 0
3 years ago
That was my grandson question I haven’t a clue what that mean
Eduardwww [97]
That would be the zero identity property. Hope it helps!

6 0
3 years ago
Simplify (4n^4 - 3n^2 + n)+ (2n^4 -7n^2 + 9n). Express your answer without factoring.
Pie

Answer:

6n^4-10n^2+10n

Step-by-step explanation:

4 n^4+2n^4-3n^2-7n^2+9n+n

6n^4-10n^2+10n

4 0
3 years ago
Read 2 more answers
How many gallons do 8 quarts equal
jeka57 [31]

it is equal to 2 gallons

7 0
3 years ago
Read 2 more answers
I arrive at a bus stop at a time that is normally distributed with mean 08:00 and SD 2 minutes. My bus arrives at the stop at an
Nimfa-mama [501]

Answer:

0.0485 = 4.85% probability that you miss the bus.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When two normal distributions are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

In this question:

We have to find the distribution for the difference in times between when you arrive and when the bus arrives.

You arrive at 8, so we consider the mean 0. The bus arrives at 8:05, 5 minutes later, so we consider mean 5. This means that the mean is:

\mu = 0 - 5 = -5

The standard deviation of your arrival time is of 2 minutes, while for the bus it is 3. So

\sigma = \sqrt{2^2 + 3^2} = \sqrt{13}

The bus remains at the stop for 1 minute and then leaves. What is the chance that I miss the bus?

You will miss the bus if the difference is larger than 1. So this probability is 1 subtracted by the pvalue of Z when X = 1.

Z = \frac{X - \mu}{\sigma}

Z = \frac{1 - (-5)}{\sqrt{13}}

Z = \frac{6}{\sqrt{13}}

Z = 1.66

Z = 1.66 has a pvalue of 0.9515

1 - 0.9515 = 0.0485

0.0485 = 4.85% probability that you miss the bus.

5 0
3 years ago
Other questions:
  • Write an expression for the situation <br><br>Number of minutes in h hours
    5·1 answer
  • Early one October, you go to a pumpkin patch to select your Halloween pumpkin. You lift the 3.4kg pumpkin to a height of 1.4m ,
    5·1 answer
  • PLEASE HELPPPP 20 POINTSSS
    14·1 answer
  • What is the constant of variation?​
    9·2 answers
  • Dawn took two pies to a school bake. She cut Pie A into 8 slices and Pie B into 6 slices. She sold two slices of Pie A and three
    8·1 answer
  • Find the magnitude of the vector with (-7, -5) and write the vector as the sum of unit vectors.
    10·2 answers
  • 5=5ax+1 please help, its due in an hour.<br><br> solve for x
    15·1 answer
  • George earns commission as a percentage of his tuxedo sales. On Tuesday, he sold $750 worth of tuxedos and earned $60
    7·1 answer
  • PLEASE HELP!!!!!! URGENT!!!!
    11·2 answers
  • Help me please !!!!!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!