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# Category Archives: Infinite Sequences

## Arithmetic & Geometric Sequence problems

*Nth* Term of a Sequence example problem

*Nth*Term of a Sequence example problem

Find a formula for the * Nth* Term of a Sequence whose first four terms are given by

(a) 4, 7, 10, 13, …

(b) 1, -3, 5, -7, …

(c)

(d)

Solution to these **Arithmetic and Geometric Sequences** practice problems is provided in the video below!

**Sequence Terms and Summation Notation example question**

Write the following Sum of the Terms of a Sequence in Summation Notation:

(a)

(b)

(c)

Solution to this **Arithmetic and Geometric Sequences** problem is provided in the video below!

**Testing For Arithmetic and Geometric Sequences example**

Determine if the following Sequences are Arithmetic, geometric or Neither:

(a)

(b)

(c)

(d)

(e)

Solution to this **Arithmetic and Geometric Sequences** problem is provided in the video below!

**Arithmetic Sequence Common Difference*** Nth* term example problem

*Nth*term example problem

For the following Arithmetic sequences, state the common difference, and write the next three terms and the ** Nth** term:

(a)

(b) -8, -5, …

(c)

Solution to this **Arithmetic and Geometric Sequences** problem is provided in the video below!

**Geometric Sequence Common Ratio*** Nth* term example question

*Nth*term example question

For the following Geometric sequences, state the common ratio, and write the next three terms and the ** Nth** term:

(a)

(b) -5, 5, -5, …

(c) 1, 1.05, …

Solution to this **Arithmetic and Geometric Sequences** problem is provided in the video below!

**Infinite Geometric Sequence SUM example**

For the following Geometric sequences, state the common ratio and find the Sum of ALL Terms (Infinite Sum), or state that the sum is undefined:

(a) 4,

(b)

(c) 36, -12, 4, …

(d) 1, 0.95, …

Solution to this **Arithmetic and Geometric Sequences** problem is provided in the video below!

**Geometric Sequence application word problem**

Suppose that $0.01 were deposited into a bank account on the first day of June, $0.02 on the second day, $0.04 on the third day, and so on in a geometric sequence.

(a) How much money would be deposited at this rate on June 30th?

(b) How much money would be in the account after this last deposit?

Solution to this **Arithmetic and Geometric Sequences** problem is provided in the video below!

## Ramanujan’s Nested Radical Theorem Proof

## Ramanujan’s Nested Radical Theorem Proof example question

Show that the given equation

holds true and follows a never-ending pattern.

Solution to this **Calculus & Precalculus Infinite Sequence** practice problem is given in the video below!

## Bounded Infinite Sequence problems

## Bounded Infinite Sequence example question

Show that the given sequence

is bounded and find its boundary value (the value that the sequence converges to).

Solution to this **Calculus & Precalculus Bounded Infinite Sequence** practice problem is given in the video below!

## Bounded Infinite Sequence example problem

Prove that the given sequence

is bounded and determine its boundary value (the value that the sequence converges to).

Solution to this **Calculus & Precalculus Bounded Infinite Sequence** practice problem is given in the video below!

## Bounded Infinite Sequence example

Show that the given sequence

is bounded and then find the boundary value that the sequence converges to.

Solution to this **Calculus & Precalculus Bounded Infinite Sequence** practice problem is given in the video below!

## Bounded Infinite Sequence example question #4

Show that the sequence

is bounded and find the boundary value the sequence converges to.

**Calculus & Precalculus Bounded Infinite Sequence** practice problem is given in the video below!

## Increasing & Decreasing Infinite Sequence problems

## Increasing & Decreasing Infinite Sequence example question

Determine whether the given sequence

increases or decreases.

Solution to this **Calculus & Precalculus Increasing & Decreasing Infinite Sequence** practice problem is given in the video below!

## Increasing & Decreasing Infinite Sequence example problem

Determine whether the sequence

increases or decreases.

Solution to this **Calculus & Precalculus Increasing & Decreasing Infinite Sequence** practice problem is given in the video below!

## Increasing & Decreasing Infinite Sequence example

Determine if the given sequence

is increasing or decreasing.

Solution to this **Calculus & Precalculus Increasing & Decreasing Infinite Sequence** practice problem is given in the video below!

## Infinite Sequences Convergence Divergence problems

## Sequence Limit Definition Convergence Proof example question

Show that the sequence

converges to 1 by Sequence Limit Definition.

Solution to this **Calculus & Precalculus Infinite Sequence Convergence** practice problem is given in the video below!

## Sequence Convergence with Squeeze Theorem example problem

Show that the sequence

converges by using the **Squeeze Theorem**.

Solution to this **Calculus & Precalculus Infinite Sequence Convergence** practice problem is given in the video below!

## Sequence Convergence Divergence example

Determine whether the sequence

converges or diverges.

Solution to this **Calculus & Precalculus Infinite Sequence Convergence** practice problem is given in the video below!

## Sequence Convergence Divergence example question #2

Determine whether the given sequence

converges or diverges.

**Calculus & Precalculus Infinite Sequence Convergence** practice problem is given in the video below!

## Sequence Convergence Divergence example problem #3

Determine whether the following sequence

converges or diverges.

**Calculus & Precalculus Infinite Sequence Convergence** practice problem is given in the video below!

## Sequence Convergence Divergence example #4

Determine whether the sequence

is convergent or divergent.

**Calculus & Precalculus Infinite Sequence Convergence** practice problem is given in the video below!

## Sequence Convergence Divergence example question #5

Determine whether the given sequence

is convergent or divergent.

**Calculus & Precalculus Infinite Sequence Convergence** practice problem is given in the video below!

## Sequence Convergence Divergence example problem #6

Determine whether the following sequence

is convergent or divergent.

**Calculus & Precalculus Infinite Sequence Convergence** practice problem is given in the video below!

## Sequence Convergence Divergence example #7

Does the sequence

converge or diverge?

**Calculus & Precalculus Infinite Sequence Convergence** practice problem is given in the video below!

## Sequence Convergence Divergence example question #8

Does the given sequence

converge or diverge?

**Calculus & Precalculus Infinite Sequence Convergence** practice problem is given in the video below!

## Sequences & Series problems (complete Playlist)

Lots of different **Sequences & Series** examples and practice problems applicable to your Calculus or Precalculus courses.

## Infinite Sequences problems (complete Playlist)

Find a variety of **Sequences** examples and practice problems for your Calculus or Precalculus courses.

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