Understanding Arithmetic and Geometric series, help?

Nov 2015
1
0
USA
Below are a few examples i pulled from by book, i was wondering if i could get some help with so i can have a better understanding on how to solve the rest.

8+3-2-7-12-....-87

1a) What Kind of series is this? Arithmetic, Geometric, or Neither? Why?

1b) Use the appropriate formula to find the explicit formula for a_n for this series?

1c) Find the number of terms in the series and the sum of S_n using an appropriate formula
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2) Given the series 4/3+1+3/4+9/16+...:
2a) What Kind of series is this? Arithmetic, Geometric, or Neither? Why?

2b) Use the appropriate formula to find the explicit formula for a_n for this series?

2c) Find the number of terms in the series and find the sum S_n or find S_∞, using an appropriate formula.

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3) Given the series 2-3/4+4/9-5/16+...;

3a) What Kind of series is this? Arithmetic, Geometric, or Neither? Why?

3b) Find the explicit formula a_n for this series and write the series in summation notations using the index i starting at n=1.

3c) how many terms in the series? why?
 
Sep 2015
27
10
New Jersey
Here are some techniques that will help:

If a series is arithmetic, the difference of any term and the preceding term is a constant.

So, in the 1st series, 3 - 8 = -5; -2 - 3 = -5; -7 - (-2) = -5. The difference is constant,

so it's an arithmetic series.

To see if a series is geometric, divide any term by the preceding term. If the ratio is

constant, the series is geometric. So in the 2nd series, 1 ÷ 4/3 = 3/4; 3/4 ÷ 1 = 3/4;

9/16 ÷ 3/4 = 3/4. The ratio is constant, so it's geometric.

Once you know the first term and the common difference or ratio, just use the appropriate

formula (you must have them!) to find the nth term or the sum.
 
Feb 2015
2,255
510
Ottawa Ontario
Google "introduction to arithmetic/geometric series".
Read up and you'll soon be an expert!