Question

Consider the geometric sequence 4, 40, 400, 4000, ...

Answer 1

The explicit formula for the nth term of the sequence will be:

$a_{n}= 4.(10)^{n-1}$

Step-by-step explanation:

We need to find the explicit formula for the nth term of the sequence :

4, 40, 400, 4000, ...

In the given sequence

First term = a₁ = 4

Common ratio = r :

40/4 = 10

400/40 = 10

4000/400 = 10

So, common ratio = r= 10

The formula used to find explicit formula will be:

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

Putting values in the formula:

$a_{n}= a_{1}.r^{n-1}\\a_{n}= 4.(10)^{n-1}$

The explicit formula for the nth term of the sequence will be:

$a_{n}= 4.(10)^{n-1}$

Keywords: Explicit formula for geometric sequence

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