The sum of first 20 arithmetic series 
Given:
Arithmetic series for 3rd term is 55
Arithmetic series for 7th term is -98
To find:
The sum of first 20 Arithmetic series
<u>Step by Step Explanation:
</u>
Solution:
Formula for calculating arithmetic series
Arithmetic series=a+(n-1) d
Arithmetic series for 3rd term 

Arithmetic series for 19th term is


Subtracting equation 2 from 1
![\left[a_{19}+18 d=-98\right]+\left[a_{1}+2 d=55\right]](https://tex.z-dn.net/?f=%5Cleft%5Ba_%7B19%7D%2B18%20d%3D-98%5Cright%5D%2B%5Cleft%5Ba_%7B1%7D%2B2%20d%3D55%5Cright%5D)
16d=-98-55
16d=-153

Also we know





First 20 terms of an AP



![a_{20}=[1106 / 16]-[2907 / 16]](https://tex.z-dn.net/?f=a_%7B20%7D%3D%5B1106%20%2F%2016%5D-%5B2907%20%2F%2016%5D)

Sum of 20 Arithmetic series is

Substitute the known values in the above equation we get
![S_{20}=\left[\frac{20\left(\left(\frac{558}{8}\right)+\left(\frac{-1801}{16}\right)\right)}{2}\right]](https://tex.z-dn.net/?f=S_%7B20%7D%3D%5Cleft%5B%5Cfrac%7B20%5Cleft%28%5Cleft%28%5Cfrac%7B558%7D%7B8%7D%5Cright%29%2B%5Cleft%28%5Cfrac%7B-1801%7D%7B16%7D%5Cright%29%5Cright%29%7D%7B2%7D%5Cright%5D)
![S_{20}=\left[\frac{\left.20\left(\frac{1106}{16}\right)+\left(\frac{-1801}{16}\right)\right)}{2}\right]](https://tex.z-dn.net/?f=S_%7B20%7D%3D%5Cleft%5B%5Cfrac%7B%5Cleft.20%5Cleft%28%5Cfrac%7B1106%7D%7B16%7D%5Cright%29%2B%5Cleft%28%5Cfrac%7B-1801%7D%7B16%7D%5Cright%29%5Cright%29%7D%7B2%7D%5Cright%5D)

![S_{20}=5\left[\frac{-695}{16}\right]](https://tex.z-dn.net/?f=S_%7B20%7D%3D5%5Cleft%5B%5Cfrac%7B-695%7D%7B16%7D%5Cright%5D)

Result:
Thus the sum of first 20 terms in an arithmetic series is 
Answer: Angle Bisector Theorem states that if a ray bisect an angle of a triangle,then it divides the opposite side into segments that are proportional to the other two side.
if this helped pls mark brainliest.
Answer:
7
Step-by-step explanation:
a right angle is 90 degrees so
90=76+2x subtract 76 from both sides
-76 -76
________
14=2x divide 2 from both sides
_ ___
2 2
7=x
Check:
76+(2*7)=90 correct
Answer:

Step-by-step explanation:
To write the equation of a circle, use the formula
where the center of the circle is (h, k).
This means the equation is
.
Find the radius r by finding the distance between (3,2) and (9,3) using the distance formula.

Since the radius is √37 and therefore
.
The equation is
.