Precalculus Examples

Find the Sum of the First 6 Terms
, , , ,
Step 1
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 gives the next term. In other words, .
Geometric Sequence:
Step 2
This is the form of a geometric sequence.
Step 3
Substitute in the values of and .
Step 4
Multiply by .
Step 5
This is the formula to find the sum of the first terms of the geometric sequence. To evaluate it, find the values of and .
Step 6
Replace the variables with the known values to find .
Step 7
Multiply by .
Step 8
Simplify the numerator.
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Step 8.1
Raise to the power of .
Step 8.2
Subtract from .
Step 9
Simplify the expression.
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Step 9.1
Subtract from .
Step 9.2
Divide by .
Step 10
Convert the fraction to a decimal.
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