Calculus Examples

3

$3$ ,

6

$6$ ,

12

$12$

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

2

$2$ gives the next term. In other words,

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

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

Geometric Sequence:

r = 2

$r = 2$

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} = 3

$a_{1} = 3$ and

r = 2

$r = 2$ .

a_{n} = 3 \cdot 2^{n - 1}

$a_{n} = 3 \cdot 2^{n - 1}$

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