Calculus Examples

$10$ , $0 {(1 + \frac{0.05}{2})}^{4}$

Step 1

Divide $0.05$ by $2$ .

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

Step 2

Add $1$ and $0.025$ .

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

Step 3

Raise $1.025$ to the power of $4$ .

$10, 0 \cdot 1.10381289$

Step 4

Multiply $0$ by $1.10381289$ .

$10, 0$

Step 5

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 10$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 10$

Step 6

This is the formula of an arithmetic sequence.

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

Step 7

Substitute in the values of $a_{1} = 10$ and $d = - 10$ .

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

Step 8

Simplify each term.

Tap for more steps...

Step 8.1

Apply the distributive property.

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

Step 8.2

Multiply $- 10$ by $- 1$ .

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

Step 9

Add $10$ and $10$ .

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

Step 10

Substitute in the value of $n$ to find the $n$ th term.

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

Step 11

Multiply $- 10$ by $3$ .

$a_{3} = - 30 + 20$

Step 12

Add $- 30$ and $20$ .

$a_{3} = - 10$