8.3 Arithmetic Series. When the terms of a sequence are, the resulting expression is a series. Example: Sequence: 3, 6, 9, 12, 15 Series: 3 + 6 + 9 +

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Presentation transcript:

8.3 Arithmetic Series

When the terms of a sequence are, the resulting expression is a series. Example: Sequence: 3, 6, 9, 12, 15 Series: You can use notation or notation to write a series. added summation

Example: i = index of summation 1 = lower limit of summation 5 = upper limit of summation read as: “the sum from i equals 1 to 5 of 3i” means the sum of the first n terms of a sequence.

Find the sum of each series. 1.

Find the sum of each series. 2.

Find the sum of each series. 3.

Find the sum of each series. 4.

Find the sum of each series. 5.

Write a series using summation notation 6.

Write a series using summation notation 7.

Write a series using summation notation 8.

Depending on what information is given, you may also need the following formula for the sum of an arithmetic series:

Use the given data about an arithmetic series to find the required value. 9.

Use the given data about an arithmetic series to find the required value. 10.

Use the given data about an arithmetic series to find the required value. 11.

12. On the Chesley farm, Mrs. Chesley gathers 34 eggs from her chickens on the first day of the month. She estimates that on each successive day of the month, the amount gathered can be six more than the preceding day. If a month is 30 days, how many eggs will she collect?

13. Kim wants to invest $40,000 so that she can buy Invisiline for her teeth over the next 16 years. She wants to invest $1,600 for the first year and increase her deposit by a fixed amount each year. What should this fixed amount be?