Calculus Examples

$1$ , $2$ , $4$ , $8$ , $16$ , $32$ , $64$ , $128$ , $256$ , $512$ , $1024$ , $2048$ , $4096$

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

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

Step 4

Multiply $2^{n - 1}$ by $1$ .

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

Step 5

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

$a_{14} = 2^{(14) - 1}$

Step 6

Subtract $1$ from $14$ .

$a_{14} = 2^{13}$

Step 7

Raise $2$ to the power of $13$ .

$a_{14} = 8192$