Finding the 9th Term of a Geometric Sequence: a9 = -781250

Calculate the 9th term (a9) for the geometric series -2, -10, -50, ... by finding the common ratio (r=5) and applying the formula an = a1(r)n-1.

Answer

The problem asks to find the 9th term (

) of the given geometric series.

The sequence is:

A geometric sequence is defined by its first term

and its common ratio

. The

-th term is given by the formula:

Step 1: Identify the first term ()
The first term of the sequence is:

Step 2: Find the common ratio ()
The common ratio

is found by dividing any term by the preceding term:

Check with the next terms:

The common ratio is

Step 3: Determine the desired term number ()
We need to find

, so

Step 4: Plug , , and into the formula
Substitute

, and

Step 5: Solve for
First, calculate

Now, substitute this value back into the equation for

The 9th term of the geometric series is

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Finding the 9th Term of a Geometric Sequence: a9 = -781250

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