Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:
![\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac2n%5Cright%5D%2C%5Cleft%5B%5Cdfrac2n%2C%5Cdfrac4n%5Cright%5D%2C%5Cleft%5B%5Cdfrac4n%2C%5Cdfrac6n%5Cright%5D%2C%5Cldots%2C%5Cleft%5B%5Cdfrac%7B2%28n-1%29%7Dn%2C2%5Cright%5D)
Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

where  . Each interval has length
. Each interval has length  .
.
At these sampling points, the function takes on values of

We approximate the integral with the Riemann sum:

Recall that

so that the sum reduces to

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

Just to check:

 
        
             
        
        
        
1/7 = 0.14285714
rounded to the nearest thousandth, it would be 0.143
        
             
        
        
        
We have that  the fourth term of an arithmetic sequence is
a_4=14
Option C
From the question we are told 
What is the fourth term of an arithmetic sequence whose first term is 23 and whose seventh term is 5?
A) 78
B) 32
C) 14
(Explain your work)
Generally the equation for the  arithmetic sequence  is mathematically given as

Therefore
For seventh term

Therefore
For Fourth term

a_4=14
For more information on this visit
brainly.com/question/23366835
 
        
             
        
        
        
Answer:
Covered: $3712
Still need to pay: $928
Step-by-step explanation:
4/5 --> 0.8 --> 80%
4640 x 0.8 --> 3712
Covered: $3712 (which is 80%)
Still need to pay: $928 (which is 20%)