Calculus Examples

$5$ , $10$ , $20$

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 $a_{1} = 5$ and $r = 2$ .

$a_{n} = 5 \cdot 2^{n - 1}$

Step 4

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

$a_{5} = 5 \cdot 2^{(5) - 1}$

Step 5

Subtract $1$ from $5$ .

$a_{5} = 5 \cdot 2^{4}$

Step 6

Raise $2$ to the power of $4$ .

$a_{5} = 5 \cdot 16$

Step 7

Multiply $5$ by $16$ .

$a_{5} = 80$

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