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Arithmetic & Geometric Sequence problems
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
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
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.
Solution to this 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.
Solution to this 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.
Solution to this 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.
Solution to this 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.
Solution to this 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.
Solution to this Calculus & Precalculus Infinite Sequence Convergence practice problem is given in the video below!
Sequence Convergence Divergence example #7
Does the sequence
converge or diverge?
Solution to this 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?
Solution to this 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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