Arithmetic And Geometric Sequences And Series Assignment.docx

Arithmetic and Geometric Sequences and Series Assignment 1. Write an equation for the nth term of each arithmetic sequence.

45, 30, 15, 0, … 2. Find the sum of the arithmetic series. 𝟏𝟎𝟏

∑(𝟒 − 𝟒𝒏) 𝒏=𝟖

3. Find the sum of the infinite series, if it exists.

𝒂𝟏 = 𝟐𝟔, 𝒓 =

𝟏 𝟐

4. Find the sum of the infinite series, if it exists.

𝟔+𝟒+

𝟖 +⋯ 𝟑

5. Find the first three terms of the arithmetic series described.

𝒂𝟏 = 𝟏, 𝒂𝒏 = 𝟏𝟗, 𝑺𝒏 = 𝟏𝟎𝟎 6. Find the sum of the arithmetic series. 𝟓

∑(𝟗 − 𝟒𝒏) 𝒏=𝟏

7. Find the first five terms of the sequence described.

𝒂𝟏 = 𝟑, 𝒂𝒏+𝟏 = 𝒂𝒏 + 𝟓 8. Find the sum of the infinite series, if it exists.

100 + 20 + 4 + ⋯ 9. Find the sum of the geometric series. 𝟑𝟐

∑[𝟗(−𝟏)𝒌−𝟏 ] 𝒌=𝟐

10. Find the indicated term of the arithmetic sequence. Find 𝒂𝟐𝟑 in the sequence −𝟏𝟖, −𝟑𝟒, −𝟓𝟎, −𝟔𝟔, … 11. Find the first three terms of the arithmetic series described.

𝒏 = 𝟏𝟔, 𝒂𝒏 = 𝟏𝟓, 𝑺𝒏 = −𝟏𝟐𝟎 12. Find the first three terms of the arithmetic series described.

𝒏 = 𝟏𝟓, 𝒂𝒏 =

𝟒 , 𝑺 = 𝟒𝟓 𝟓 𝒏

13. Find the sum of the infinite series, if it exists.

−𝟐𝟕𝟎 + 𝟏𝟑𝟓 − 𝟔𝟕. 𝟓 + ⋯ 14. Find the first three terms of the arithmetic series described.

𝑺𝒏 = 𝟒𝟖𝟔𝟎, 𝒓 = 𝟑, 𝒂𝒏 = 𝟑𝟐𝟖𝟎. 𝟓