8.2: Arithmetic Sequences and Partial Sums

ObjectivesSWBAT

•Recognize, write, and find the nth terms of arithmetic sequences. •Find the nth partial sums of arithmetic sequences. •Use arithmetic sequences to model and solve real-life problems.

Vocabulary/Key Concepts

Arithmetic Sequence Common Difference

Sum of a Finite Arithmetic Sequence

1. an =45n +12

1 2 3 4 5 6 7 8 9 10nan

Use the table feature of a graphing utility to find the first 10 terms of the sequence.

3. 1,3,5,7,...,199

4. −10,−9,−8,...,50

2. 1+ 4 + 7 +10 +13+16 +19Find the sum of the finite arithmetic sequence.

Sum of Finite Arithmetic Seq.

Sn =n2a1 + an( )

6. nn=51

100

∑ − nn=1

50

∑

7. 1000 − n( )n=0

250

∑

5. 2nn=1

100

∑Find the partial sum without a graphing utility.

Sum of Finite Arithmetic Seq.

Sn =n2a1 + an( ) 9. 10.5 + 0.025 j( )

j=1

200

∑8. 50 − 2n( )n=0

50

∑Use a graphing utility to find the partial sum.

10. Number of Logs Logs are stacked in a pile, as shown in the figure. The row has 15 logs and the bottom row has 24 logs. How many logs are in the pile?