Calculus Examples

1

$1$ ,

5

$5$ ,

25

$25$ ,

125

$125$

Step 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by

5

$5$ gives the next term. In other words,

a_{n} = a_{1} r^{n - 1}

$a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence:

r = 5

$r = 5$

Step 2

This is the form of a geometric sequence.

a_{n} = a_{1} r^{n - 1}

$a_{n} = a_{1} r^{n - 1}$

Step 3

Substitute in the values of

a_{1} = 1

$a_{1} = 1$ and

r = 5

$r = 5$ .

a_{n} = 1 \cdot 5^{n - 1}

$a_{n} = 1 \cdot 5^{n - 1}$

Step 4

Multiply

5^{n - 1}

$5^{n - 1}$ by

1

$1$ .

a_{n} = 5^{n - 1}

$a_{n} = 5^{n - 1}$