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Solved problems for the chapter:

Arithmetic Sequences

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Infinite sequence

1. Near point

2. Infinite sequence limit

2.1. Convergence sequence

2.2. Divergent sequence

2.3. Limit of a sequence

3. Evaluation of limits

3.1. Euler's number

4. Forum

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Arithmetic sequence

1. General term of an arithmetic sequence

1.1. Common difference of the Arithmetic sequence

1.1.1. Increasing / decreasing arithmetic sequence

2. Arithmetic mean

3. Linear interpolation

4. Forum

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Geometric sequence

1. General term of a geometric sequence

1.1. Common ratio of a geometric sequence

2. Geometric mean

2.1. Relationship between geometric and arithmetic mean

2.1.1. Numerical Proof

2.1.2. Graphical proof

3. Forum

↓ Show theory [3] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:arithmetic_sequences/4744/

Example 1.

The sequence is given

Find out what type of sequence it is.
Calculate the limit: .

Example 2.

We have a sequence with the general term .

Calculate the limit of the sequence.
Find out which members of the sequence lie inside the ?

The following sequence is given:

Calculate its limit, if any.
How many members of the sequence are outside the - neighborhood limits for ?

Given a sequence whose general term is:

and its limit equal to , determine which members of the sequence satisfy the condition .

Show that for the values of the expressions are consecutive terms of an arithmetic sequence. Write down the common difference of the sequence.

The zeros of the polynomial are the first three terms of a geometric sequence. Write down the zeros and general terms of the geometric sequence.

Calculate for which real numbers x are the values of the given expressions consecutive terms of the arithmetic sequence:

Calculate the geometric mean of the numbers and .

Calculate for which real numbers of x are the values of the given expressions consecutive terms of an arithmetic sequence:

10.

Calculate the geometric mean of the numbers and .

11.

Calculate for which real numbers x are the values of the given expressions consecutive terms of the arithmetic sequence:

12.

Calculate for which real numbers x are the values of the given expressions consecutive terms of the arithmetic sequence:

13.

Calculate for which real numbers x are the values of the given expressions are consecutive terms of an arithmetic sequence:

14.

Calculate for which real numbers x are the values of the given expressions consecutive terms of an arithmetic sequence:

15.

Calculate for which real numbers x are the values of the given expressions consecutive terms of an arithmetic sequence:

16.

Calculate to what term are the terms of the sequence greater than ?

17.

Solution of the equation is the first term, solution of the equation is the second term of a geometric sequence. Write down the common ratio of the sequence.