# Calculus Examples

Find the Sum of the First 6 Terms
, , , ,
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:
This is the form of a geometric sequence.
Substitute in the values of and .
Multiply by to get .
Remove parentheses around .
This is the formula to find the sum of the first terms of the geometric sequence. To evaluate it, find the values of and .
Replace the variables with the known values to find .
Multiply by to get .
Simplify the numerator.
Remove parentheses around .
Raise to the power of to get .
Subtract from to get .
Simplify the denominator.
Remove parentheses.
Subtract from to get .
Divide by to get .
Convert the fraction to a decimal.

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