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
Alenkasestr [34]
3 years ago
15

Write the explicit formula for the nth term of the arithmetic sequence 14, 28, 42.56

Mathematics
1 answer:
natka813 [3]3 years ago
7 0

Answer:

The explicit formula of the given AP is  a(n)  = 7 + 7 n

And the term  a (13)  = 98

Step-by-step explanation:

Here, the given sequence  is :  14, 28 , 42, 56 ,....

First Term (a)  = 14

Second term = 28

Now, the Common difference (d) = Second term - First Term

                                                      = 28 - 14 = 14

Now, the formula for nth term in an AP is :      a(n) = a + (n-1)d

So, here, the nth term of the sequence is given as:

a(n)  = 14  + (n-1) 7  

          = 14 + 7 n - 7 =  7 + 7 n

or, a(n)  = 7 + 7 n ......... (1)

or, The explicit formula of the given AP is  a(n)  = 7 + 7 n

Now, for evaluating a (13) put n = 13 in (1)

⇒ a(13)  = 7 +  7 (13) =  7 + 91  = 98

or, a (13)  = 98

You might be interested in
Find the 52nd term of the arithmetic sequence ?
Gwar [14]

不完整的问题,对不起,伙计。

本题已由中国数学会官方解答(现有会员:2人)

3 0
2 years ago
Read 2 more answers
2 yards and 60 inches in ratio
arsen [322]

2yrds:60in    is the answer


8 0
3 years ago
What is the square root of 864
skelet666 [1.2K]

There are two ways to evaluate the square root of 864: using a calculator, and simplifying the root.

The first method is simplifying the root. While this doesn't give you an exact value, it reduces the number inside the root.

Find the prime factorization of 864:

\sqrt{864} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3}

Take any number that is repeated twice in the square root, and move it outside of the root:

\sqrt{864} = \sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3}

\sqrt{2 \cdot 2} = \sqrt{4} = 2

\sqrt{3 \cdot 3} = \sqrt{9} = 3

\sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3} = \sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3}

\sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3} = (2 \cdot 2 \cdot 3) \sqrt{2 \cdot 3} = \boxed{12 \sqrt{6}}

The simplified form of √864 will be 12√6.

The second method is evaluating the root. Using a calculator, we can find the exact value of √864.

Plugged into a calculator and rounded to the nearest hundredths value, √864 is equal to 29.39. Because square roots can be negative or positive when evaluated, this means that √864 is equal to ±29.39.

6 0
3 years ago
What is the relationship between the lines determined by the following two equations?
oksano4ka [1.4K]

Answer:

C. They are the same line.

Step-by-step explanation:

In order to compare the linear equations given, they need to be in the same form.  The best form in order to evaluate slope and y-intercept is slope-intercept form, y = mx + b.  Since the second equation is already in slope-intercept form, we need to use inverse operations to convert the first equation:

6x - 2y = 16 ----  6x - 2y - 6x = 16 - 6x ----  -2y = -6x + 16

-2y/-2 = -6x/-2 + 16/-2

y = 3x - 8

Since both equations are in the form y = 3x - 8, then they are both the same line.

4 0
3 years ago
A county's population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using the exponential
aliina [53]
Let t=number of years since 1991.
Then 
P(t)=147 e^(kt)   ... in millions
P(0)=147 e^(0)=147
P(7)=147 e^(7k)=153
e^(7k)=(153/147)
take ln both sides
ln(e^(7k))=ln(153/147)
7k=0.0400 => k=0.005715

Year 2017=>t=2017-1991=26
P(26)=147e^(26*.005715)=170.55
Answer: in 2017, the projected population is 170.55 millions.
6 0
3 years ago
Other questions:
  • Plz help with math!!!
    6·1 answer
  • 9:45 on Tuesday Questions
    14·1 answer
  • G + 15.5 = -23.4 solve for g
    8·2 answers
  • Why does all heads or all tails seem less likely than random?
    14·1 answer
  • Find the exact value of sin 165º.
    10·2 answers
  • 17 Q Graph the inequality n a coordinate plane
    11·1 answer
  • What is the equation used to find the slope of two points?
    12·1 answer
  • Can you help me with this plz
    6·2 answers
  • Answer attached problem ​
    10·1 answer
  • The income of Anny's family in 2008 is Php 65 000.00. From 2008 to 2011, the income of the family increased by 20% per year. Wha
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!