Algebra Examples

1

$1$ ,

2

$2$ ,

4

$4$ ,

8

$8$ ,

16

$16$ ,

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} = 1

$a_{1} = 1$ and

r = 2

$r = 2$ .

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

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

Step 4

Multiply

2^{n - 1}

$2^{n - 1}$ by

1

$1$ .

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

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

Step 5

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{6} = 2^{(6) - 1}

$a_{6} = 2^{(6) - 1}$

Step 6

Subtract

1

$1$ from

6

$6$ .

a_{6} = 2^{5}

$a_{6} = 2^{5}$

Step 7

Raise

2

$2$ to the power of

5

$5$ .

a_{6} = 32

$a_{6} = 32$