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Notes
Questions
\(\textbf{1)}\) \(\displaystyle\sum_{i=3}^{5}3-2i\)
\(\textbf{2)}\) \(\displaystyle\sum_{n=4}^{9}3i-5\)
\(\textbf{3)}\) \(a_1=3,\, d=5,\,\) what are \(a_8\) and \(S_8\)?
\(\textbf{4)}\) \(a_1=4,\, a_5=10,\,\) what are \(d\) and \(S_8\)?
\(\textbf{5)}\) \(a_6=22,\, S_6=90,\,\) what is \(a_1\)?
\(\textbf{6)}\) \(3+9+15+ \cdots +75=\)
\(\textbf{7)}\) Find the sum of the first 18 terms of \(5,8,11,14,17…\)
\(\textbf{8)}\) Find the sum of the first 12 terms of \(-6,-4,-2,0,2…\)
\(\textbf{9)}\) Find the sum of the first 30 terms of \(-10,-7,-4,-1,2…\)
\(\textbf{10)}\) The sum of the first two terms is \(8\), the sum of the first three terms is \(15
\), what is the value of the first term, \(a_1\)?
See Related Pages
\(\bullet\text{ Arithmetic Sequences}\)
\(\,\,\,\,\,\,\,a_n=a_1 + d(n-1)\)
\(\bullet\text{ Geometric Sequences}\)
\(\,\,\,\,\,\,\,a_n=a_1 \cdot r^{(n-1)}…\)
\(\bullet\text{ Geometric Series}\)
\(\,\,\,\,\,\,\,s_n=a_1 \frac{1-r^n}{1-r}…\)
\(\bullet\text{ Infinite Geometric Series}\)
\(\,\,\,\,\,\,\,s_\infty = \frac{a_1}{1-r}\,\,\, |r| \lt 1…\)
\(\bullet\text{ Summation Notation}\)
\(\,\,\,\,\,\,\, \displaystyle \sum_{i=4}^{9} 3i-5 …\)
\(\bullet\text{ Recursive Sequences}\)
\(\,\,\,\,\,\,\, a_{1}=2, \, a_{n+1}=a_{n}+3…\)
In Summary
An arithmetic series is a sequence of numbers in which each term is the sum of the previous term and a fixed constant. The constant is called the common difference, and the sequence is called an arithmetic sequence. This is typically studied in math classes such as algebra and pre-calculus. They are an important topic in these courses because they provide a foundation for more advanced mathematical concepts, and have many real world applications.
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Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.
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