Find the 4th Term 0.1 , 0.01 , 0.001

$0.1$ , $0.01$ , $0.001$

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 $0.1$ gives the next term. In other words, $a_{n} = a_{1} \cdot r^{n - 1}$ .

Geometric Sequence: $r = 0.1$

This is the form of a geometric sequence.

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

Substitute in the values of $a_{1} = 0.1$ and $r = 0.1$ .

$a_{n} = (0.1) \cdot {(0.1)}^{n - 1}$

Multiply $0.1$ by ${(0.1)}^{n - 1}$ by adding the exponents.

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Multiply $0.1$ by ${(0.1)}^{n - 1}$ .

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Raise $0.1$ to the power of $1$ .

$a_{n} = 0.1 \cdot {(0.1)}^{n - 1}$

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

$a_{n} = {0.1}^{1 + n - 1}$

Combine the opposite terms in $1 + n - 1$ .

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Subtract $1$ from $1$ .

$a_{n} = {0.1}^{n + 0}$

Add $n$ and $0$ .

$a_{n} = {0.1}^{n}$

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

$a_{4} = {0.1}^{4}$

Raise $0.1$ to the power of $4$ .

$a_{4} = 0.0001$

Find the 4th Term 0.1 , 0.01 , 0.001

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