How can you use the formula for a finite geometric series in a practical situation?

The finite geometric series formula is a(1-rⁿ)/(1-r).

The sum S_{n}Sn of n terms of a geometric series with first term a_{1}a1 and common ratio rr is given by

S_{n}=a_{1}\cdot \dfrac{r^{n}-1}{r-1}Sn=a1⋅r−1rn−1

It can be used in any situation involving the accumulated consequences of exponential growth. In finance, it is used to find the future value of a sequence of payments subject to compound interest.

For example, consider 10 deposits of 1000 made at the end of the year into an account paying 2% compounded annually. The result of such a sequence of payments will be

S_{10}=\$1000\cdot \dfrac{1.02^{10}-1}{1.02-1}=\$10,949.72S10=$1000⋅1.02−11.0210−1=$10,949.72

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center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.