# Calculus Examples

,

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

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

Add and .

Step 10

Replace the variables with the known values to find .

Step 11

Step 11.1

Cancel the common factor.

Step 11.2

Rewrite the expression.

Step 12

Step 12.1

Multiply by .

Step 12.2

Add and .

Step 13

Convert the fraction to a decimal.