Algebra Examples

3

$3$ ,

15

$15$ ,

75

$75$ ,

375

$375$

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

5

$5$ gives the next term. In other words,

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

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

Geometric Sequence:

r = 5

$r = 5$

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 = 5

$r = 5$ .

a_{n} = 3 \cdot 5^{n - 1}

$a_{n} = 3 \cdot 5^{n - 1}$

Step 4

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{5} = 3 \cdot 5^{(5) - 1}

$a_{5} = 3 \cdot 5^{(5) - 1}$

Step 5

Subtract

1

$1$ from

5

$5$ .

a_{5} = 3 \cdot 5^{4}

$a_{5} = 3 \cdot 5^{4}$

Step 6

Raise

5

$5$ to the power of

4

$4$ .

a_{5} = 3 \cdot 625

$a_{5} = 3 \cdot 625$

Step 7

Multiply

3

$3$ by

625

$625$ .

a_{5} = 1875

$a_{5} = 1875$

3, 15, 75, 375

$3, 15, 75, 375$

(

)

[

]

√



≥

















≤















∩

∪







∞











