Calculus Examples

Find the Sum of the First 6 Terms
, , , ,
Step 1
This is the formula to find the sum of the first terms of the sequence. To evaluate it, the values of the first and th terms must be found.
Step 2
This is an arithmetic sequence since there is a common difference between each term. In this case, adding to the previous term in the sequence gives the next term. In other words, .
Arithmetic Sequence:
Step 3
This is the formula of an arithmetic sequence.
Step 4
Substitute in the values of and .
Step 5
Simplify each term.
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Step 5.1
Apply the distributive property.
Step 5.2
Multiply by .
Step 6
Subtract from .
Step 7
Substitute in the value of to find the th term.
Step 8
Multiply by .
Step 9
Subtract from .
Step 10
Replace the variables with the known values to find .
Step 11
Add and .
Step 12
Cancel the common factor of .
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Step 12.1
Factor out of .
Step 12.2
Cancel the common factor.
Step 12.3
Rewrite the expression.
Step 13
Multiply by .
Step 14
Convert the fraction to a decimal.
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