Juan purchased an antique that had a value of \$200$200dollar sign, 200 at the time of purchase. Each year, the value of the antique is estimated to increase 10\%10%10, percent over its value the previous year. The estimated value of the antique, in dollars, 222 years after purchase can be represented by the expression 200a200a200, a, where aaa is a constant. What is the value of aaa ?

Step-by-step explanation:

At the time of purchase, the value of the antique is $200.

After one year the value will increase 10%.

Hence, after one year, the value of the antique will be = 220.

Similarly, after two year, the value will be .

Thus, 222 years after purchase, the value of the antique will be .

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

your answer would be 12