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Finding the 9th Term of a Geometric Sequence: a9 = -781250
Published on March 30, 2026
Algebra
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.
Question
Answer
The problem asks to find the 9th term (
The sequence is:
A geometric sequence is defined by its first term
Step 1: Identify the first term (
The first term of the sequence is:
The first term of the sequence is:
Step 2: Find the common ratio (
The common ratio
The common ratio
Check with the next terms:
The common ratio is
Step 3: Determine the desired term number (
We need to find
We need to find
Step 4: Plug
Substitute
Substitute
Step 5: Solve for
First, calculate
First, calculate
Now, substitute this value back into the equation for
The 9th term of the geometric series is