Calculus Examples

$8$ , $16$ , $32$

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 $2$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 2$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 8$ and $r = 2$ .

$a_{n} = 8 \cdot 2^{n - 1}$

Step 4

Multiply $8 \cdot 2^{n - 1}$ .

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Step 4.1

Rewrite $8$ as $2^{3}$ .

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

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a_{n} = 2^{3 + n - 1}$

Step 4.3

Subtract $1$ from $3$ .

$a_{n} = 2^{n + 2}$

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