Answer:
The sum of the given series is 1023
Step-by-step explanation:
Geometric series states that a series in which a constant ratio is obtained by multiplying the previous term.
Sum of the geometric series is given by:
where a is the first term and n is the number of term.
Given the series:
This is a geometric series with common ratio(r) = 2
We have to find the sum of the series for 10th term.
⇒ n = 10 and a = 1
then;
Therefore, the sum of the given series is 1023
Answer:
The equation of circle is +
= 18
Step-by-step explanation:
Given the endpoints of the diameter of a circle: (-2,-3) and (4,-1)
We know that the equation of circle is
+
=
where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.
To find (h,k): the center is midpoint of diameter
Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by
( ,
)
( ,
)
(1,2)
Hence (h,k) is (1,2)
Substituting values of (h.k) and (x.y) as (1,2) and (4,-1) respectively in equation of circle, we get
+
=
= 18
Now substituting values of (h,k) and in equation of circle, we get
+
= 18
Hence the equation of circle is +
= 18