The Geometric Series

Geometric sequences

$\rhd$ Introduction to geometric sequences (10:44) Recognizing a geometric sequence, the initial term and common ratio.
$\rhd$ Introduction to geometric sequences (advanced) (6:38) An emphasis on the notation is given to deduce the $n^{\mathrm{th}}$ term of the sequence.
$\rhd$ Explicit and recursive formulas for geometric sequences (5:37) Find explicit and recursive formulas for the $n^{\mathrm{th}}$ term of the sequence $\{168, 84, 42, 21, \dots\}$ .
* Practice: Explicit formulas for geometric series. (4 problems)

Geometric series

$\rhd$ Introduction to geometric series (6:16) Using a savings account as an application of geometric series.
$\rhd$ Geometric series (2:52) Using the sigma notation to represent the sum of the terms of the sequence.
$\rhd$ Finite geometric series (7:14) Deriving a formula for a finite geometric series.
Evaluate a finite geometric series (6:54)
1. Find the sum of the first $50$ terms in the sequence: $1+\dfrac{10}{11} + \dfrac{100}{121}+\cdots$ .
2. Evaluate $1-0.99+0.99^2-0.99^3+\cdots -0.99^{79}$ .
3. Find the sum of the first $30$ terms in the sequence given by $a_1=10$ and $a_i = a_{i-1}\dfrac{9}{10}$ .
* Practice: Geometric series formula. (4 problems)

The OpenLab at City Tech:A place to learn, work, and share

The OpenLab is an open-source, digital platform designed to support teaching and learning at City Tech (New York City College of Technology), and to promote student and faculty engagement in the intellectual and social life of the college community.

The OpenLab at City Tech:A place to learn, work, and share

The OpenLab at City Tech:A place to learn, work, and share

Support

Accessibility

Copyright

Creative Commons

The OpenLab at City Tech:A place to learn, work, and share

Support

Accessibility

Copyright

Creative Commons