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3 years ago

12

Jasmine is saving money for her retirement. She is going to deposit $1900 in a savings account every year for the next 12 years.

The account pays 4% interest compounded annually. What will be the final value of the account after 12 years?

1 answer:

Alja [10]3 years ago

3 0

$2,812 will be the final value of the account

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Answer:

Part 15) The next three terms are 5/8,3/4 and 7/8

Part 16) The 37th term is -35.5

Step-by-step explanation:

we know that

In an <u>Arithmetic Sequence</u> the difference between one term and the next is a constant and this constant is called the common difference (d)

Part 15) Find the next three terms of the arithmetic sequence

$\frac{1}{8},\frac{1}{4},\frac{3}{8},\frac{1}{2},...$

so

$a1=1/8\\ a2=1/4\\ a3=3/8\\ a4=1/2\\ a2-a1=1/4-1/8=1/8\\ a3-a2=3/8-1/4=1/8\\ a4=a3=1/2-3/8=1/8$

The common difference is equal to

d=1/8

<u><em>Find the next three terms of the arithmetic sequence</em></u>

<u><em>Find a5</em></u>

$a5=a4+d$ -----> $a5=1/2+1/8=5/8$

<u><em>Find a6</em></u>

$a6=a5+d$ -----> $a6=5/8+1/8=3/4$

<u><em>Find a7</em></u>

$a7=a6+d$ -----> $a7=3/4+1/8=7/8$

therefore

The next three terms are

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Part 16) what is the 37th term of the arithmetic sequence

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so

$a1=4.1\\ a2=3\\ a3=1.9\\ a4=0.8$

$a2-a1=3-4.1=-1.1\\ a3-a2=1.9-3=-1.1\\ a4=a3=0.8-1.9=-1.1$

The common difference is equal to

d=-1.1

We can write an Arithmetic Sequence as a rule

$an=a1+d(n-1)$

substitute the values

$an=4.1-1.1(n-1)$

For n=37

substitute

$a37=4.1-1.1(37-1)$

$a37=4.1-1.1(36)$

$a37=-35.5$

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