# What is the nth term of the geometric sequence 5,15,45,135?

Each time, the term is three times the last, which is written mathematically as

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To find the nth term of a geometric sequence, we use the formula:

[ a_n = a_1 \times r^{(n-1)} ]

Where:

- ( a_n ) is the nth term of the sequence.
- ( a_1 ) is the first term of the sequence.
- ( r ) is the common ratio of the sequence.
- ( n ) is the term number.

In the given sequence, the first term (( a_1 )) is 5, and the common ratio (( r )) can be found by dividing any term by its preceding term. Let's use the second and first terms:

[ r = \frac{15}{5} = 3 ]

Now, we can find the nth term:

[ a_n = 5 \times 3^{(n-1)} ]

So, the nth term of the geometric sequence 5, 15, 45, 135 is ( a_n = 5 \times 3^{(n-1)} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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