Arithmetic sequences and Series

Disclaimer: The material in the videos below comes mainly from outside City Tech. The presentation in these videos may differ from the one given in your class. Please consult with your instructor to confirm whether a particular approach is acceptable in your class.

Arithmetic sequences

1. $\rhd$ Introduction to sequences (8:17) For the sequences $\{1,4,7,10\}$ and $\{3,7,11,15\ldots\}$, the notation used to indicate a term of the sequence and a formula for it are discussed.
2. $\rhd$ Introduction to arithmetic sequences (7:06) Recognizing arithmetic sequences, the initial term and their common difference.  Explicit and recursive formulas are discussed.
3. * Practice: Extend arithmetic sequences. (4 problems)
4. * Practice: Explicit formulas for arithmetic sequences. (4 problems)
5. $\rhd$ Explicit formulas for arithmetic sequences (6:16) Deriving a formula for the sequence $\{-100,-50,0,50, \dots\}$.
6. * Practice: Recursive formulas for arithmetic sequences. (4 problems)

Arithmetic series

1. $\rhd$ Summation notation (4:26)
   1. Writing $1+2+\cdots+10$ using the summation (sigma) notation.
   2. Writing $1+2+\cdots+100$ using the summation (sigma) notation.
   3.  Expanding $\displaystyle\sum_{i=0}^{50}\pi i^2$.
2. $\rhd$ Arithmetic series intro (3:55) The sum of the first $n$ terms in the sequence $\{1,2,3,\dots\}$.
3. $\rhd$ Arithmetic series formula (7:46) The sum of the first $n$ terms in the sequence $\{a, a+d, a+2d,\dots\}$.
4. $\rhd$ Arithmetic series (sigma notation) (7:01) Find $\displaystyle\sum_{k=1}^{550}(2k+50)$.
5. $\rhd$ Arithmetic series (sum expression) (6:46) Find $(-50)+(-44)+(-38)+\dots +2044$.
6. $\rhd$ Arithmetic series (recursive formula) (5:20) Given that $a_1=4$ and $a_i=a_{i-1}+11$, find the sum of the first $650$ terms of the sequence.
7. * Practice: Arithmetic series. (4 problems)
8. $\rhd$ Find sum of arithmetic sequence (4:01) Find the sum of the first 70 terms of the arithmetic sequence $22, 19, 16, 13, \dots$.