Calculus Examples

10

$10$ ,

0 {(1 + \frac{0.05}{2})}^{4}

$0 {(1 + \frac{0.05}{2})}^{4}$

Step 1

Divide

0.05

$0.05$ by

2

$2$ .

10, 0 {(1 + 0.025)}^{4}

$10, 0 {(1 + 0.025)}^{4}$

Step 2

Add

1

$1$ and

0.025

$0.025$ .

10, 0 \cdot {1.025}^{4}

$10, 0 \cdot {1.025}^{4}$

Step 3

Raise

1.025

$1.025$ to the power of

4

$4$ .

10, 0 \cdot 1.10381289

$10, 0 \cdot 1.10381289$

Step 4

Multiply

0

$0$ by

1.10381289

$1.10381289$ .

10, 0

$10, 0$

Step 5

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

- 10

$- 10$ to the previous term in the sequence gives the next term. In other words,

a_{n} = a_{1} + d (n - 1)

$a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence:

d = - 10

$d = - 10$

Step 6

This is the formula of an arithmetic sequence.

a_{n} = a_{1} + d (n - 1)

$a_{n} = a_{1} + d (n - 1)$

Step 7

Substitute in the values of

a_{1} = 10

$a_{1} = 10$ and

d = - 10

$d = - 10$ .

a_{n} = 10 - 10 (n - 1)

$a_{n} = 10 - 10 (n - 1)$

Step 8

Simplify each term.

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Step 8.1

Apply the distributive property.

a_{n} = 10 - 10 n - 10 \cdot - 1

$a_{n} = 10 - 10 n - 10 \cdot - 1$

Step 8.2

Multiply

- 10

$- 10$ by

- 1

$- 1$ .

a_{n} = 10 - 10 n + 10

$a_{n} = 10 - 10 n + 10$

a_{n} = 10 - 10 n + 10

$a_{n} = 10 - 10 n + 10$

Step 9

Add

10

$10$ and

10

$10$ .

a_{n} = - 10 n + 20

$a_{n} = - 10 n + 20$

Step 10

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{3} = - 10 \cdot 3 + 20

$a_{3} = - 10 \cdot 3 + 20$

Step 11

Multiply

- 10

$- 10$ by

3

$3$ .

a_{3} = - 30 + 20

$a_{3} = - 30 + 20$

Step 12

Add

- 30

$- 30$ and

20

$20$ .

a_{3} = - 10

$a_{3} = - 10$