John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times as the amount he paid the month betore. Explain to Jo howto represent his first 20 payment n sigma notation.Then esplain how to tind the sum of his frst 20 pyments, using complete sentences. Esplain why this series is convergent or divergent

Answers

Answer 1

Answer: Since each term of the series is 1.1 times the previous one, the series is geometric. The generic term of a geometric series is
$a_(n)=a_(0)\cdot r^((n-1))$

The sum in sigma notation simply adds these terms. The leading factor of 100 can be factored out.
$sum=\displayform{100\cdot\sum\limits_(n=1)^(20){1.1^((n-1))}}$

The sum can be found by adding the terms or by using the formula for the sum of a geometric series. In the latter case, we have
$sum=100\cdot(1.1^(20)-1)/(1.1-1)\approx5727.50$

The series is divergent because the common ratio of terms is greater than 1. (Of course, any finite number of terms will have a finite sum.)

Related Questions

Easy pointsBefore you answer this question try and rotate your foot clockwise and write the number six. Hard right.Math question now.When I am 6 my brother is half my age. How old will my brother be when I am 70?
A line has a slope of $-7$ and contains the point $(3,0)$. The equation of this line can be written in the form $y = mx+b$. What is the value of $m+b$?
A repair person is scheduled to be at your apartment between 9:00am to 12:00pm but you have to leave at 11:30 to help out a friend. If the repair person is equally likely to be at your apartment any time during the appointment time, what is the probability that you will be there?
Can someone help me on my last problem? #10
Solve the following system of equations using the elimination method.7x + 20y = 142x – 10y = 4Question 18 options:A) (3,1)B) (2,0)C) (4,–5)D) (–3,4)

Help please !!!! ASAP

Answers

Answer: 1: cant figure out sorry :(

2: 2.5

3: 5

4: 20

5: 25

10: 50

Step-by-step explanation: What i did here was divided by 5 the numbers below 3 and multiply by 5 for the numbers above 3. Hope this helps :)

A zoo has a circular pool for its seals. The diameter of the pool is 32 feet. How much fence is needed to enclose the pool?

Answers

Answer:

The answer is $32 \pi\ feet$ or $100.53\ feet$

Step-by-step explanation:

we know that

To calculate how much fence is needed to enclose the circular pool, find the circumference of the circular pool

The circumference of a circle is equal to

$C=\pi D$

where

D is the diameter of the circle

In this problem we have

$D=32\ feet$

Substitute

$C=\pi (32)=32 \pi\ feet$

$C=32 \pi\ feet=100.53\ feet$

9 + 1.34 + .5 (3.50 +1.74) How would you simplify the expression? Explain your steps.

Answers

1. Using PEMDAS, I would first solve the equation inside the parenthesis
(3.50+1.74)= 5.24
Now the equation is:
9+1.34+.5(5.24)
2. Multiply .5(5.24)
9+1.34+2.62=
12.96

What is the sum of 18 23/30+ 2/3

Answers

Answer:

See image

Step-by-step explanation:

Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. What is q?

Answers

Answer:

q = 0.105uC

Step-by-step explanation:

We can determine the force on one ball by assuming two balls are stationary, finding the E field at the lower right vertex and calculate q from that.

Considering the horizontal and vertical components.

First find the directions of the fields at the lower right vertex. From the lower left vertex the field will be at 0° and from the top vertex, the field will be at -60° or 300° because + charge fields point radially outward in all directions. The distances from both charges are the same since this is an equilateral triangle. The fields have the same magnitude:

E=kq/r²

Where r = 20cm

= 20/100

= 0.2m

K = 9.0×10^9

9.0×10^9 × q /0.2²

9.0×10^9/0.04

2.25×10^11 q

These are vector fields of course

Sum the horizontal components

Ecos0 + Ecos300 = E+0.5E

= 1.5E

Sum the vertical components

Esin0 + Esin300 = -E√3/2

Resultant = √3E at -30° or 330°

So the force on q at the lower right corner is q√3×E

The balls have two forces, horizontal = √3×E×q

and vertical = mg, therefore if θ is the angle the string makes with the vertical tanθ = q√3E/mg

mg×tanθ = q√3E.

..1

Then θ will be...

Since the hypotenuse = 80cm

80cm/100

= 0.8m

The distance from the centroid to the lower right vertex is 0.1/cos30 =

0.1/0.866

= 0.1155m

Hence,

0.8×sinθ = 0.1155

Sinθ = 0.1155/0.8

Sin θ = 0.144375

θ = arch sin 0.144375

θ = 8.3°

From equation 1

mg×tanθ = q√3E

g = 9.8m/s^2

m = 3.0g = 0.003kg

0.003×9.8×tan(8.3)

0.00428 = q√3E

0.00428 = q×1.7320×E

Where E=kq/r²

Where r = 0.2m

0.0428 = kq^2/r² × 1.7320

K = 9.0×10^9

0.0428/1.7320 = 9.0×10^9 × q² / 0.2²

0.02471×0.04 = 9.0×10^9 × q²

0.0009884 = 9.0×10^9 × q²

0.0009884/9.0×10^9 = q²

q² = 109822.223

q = √109822.223

q = 0.105uC

Perform the operation. (10x2 – 10x – 6) + (x+6)

Answers

Answer:

10x² - 9x

Step-by-step explanation:

(10x² - 10x - 6) + (x + 6)

10x² - 10x - 6 + x + 6

10x² - 9x - 6 + 6

10x² - 9x

Other Questions

A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 141 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)

An island has a popularity of 1500 and is growing at a rate of 3% per year. what will the popularity be after 6 years?Ans:1791

Let h be the function given by h(x) =x+x-2 ²-1 We will investigate the behavior of both the numerator and denominator of h(x) near the point where x = 1. Let f(x)= x³ + x -2 and g(x)=x²-1. Find the local linearizations of f and g at a = 1, and call these functions Lf(x) and Lg(x), respectively. Lf(x) = L₂(x) = Explain why h(x) ≈ Lf(x) Lg(x) for a near a = 1.

Describe which strategy you would use to divide 48 by 8