Finite Arithmetic Series
Read this topicExplanations 5
- An arithmetic series is the sum of all the specified terms in an arithmetic sequence. These series may be finite or infinite. All arithmetic series may be defined in the form ∑n…
By Bill Zhang, Qinzhuo Zhang, Alex Federspiel, Ruiran Xun, Anusha Rahman
- Arithmetic series are defined to be the sums of the terms of arithmetic sequences. For example, in the sequence 2,5,8,112,5,8,112,5,8,11, the sum of the terms is 26. Let's take …
By Vincent Huang, Ruiran Xun, Anusha Rahman
- Take your favorite arithmetic sequence, such as 10,15,20,25,30,35,4010, 15, 20, 25, 30, 35, 4010,15,20,25,30,35,40. 10+15+20+25+30+35+4010+15+20+25+30+35+4010+15+20+25+30+35+40 …
By Misha Lavrov, Eric Zhang, Expii Team, Alex Federspiel, Anusha Rahman
- Finite Arithmetic Series As we learned earlier, a series is the sum of all terms in an arithmetic sequence. We've learned that with geometric series. We can easily calculate the…
By Anusha Rahman
- (Video) Finding the Sum or an Arithmetic Series by Brian McLogan In this video by Brian McLogan you will use summation notation to find the arithmetic series.
By Anusha Rahman
Problems 13
- What is the value of ∑n=250(2n+3)\sum_{n=2}^{50}(2n+3)∑n=250(2n+3)?
- Let a1,a2,…,a2013a_1,a_2,\dots, a_{2013}a1,a2,…,a2013 be a permutation of the numbers from 111 to 201320132013. Let An=a1+a2+⋯+annA_n = \frac{a_1 + a_2 + \cdots + a_n} {n}An…
- There exists a unique strictly increasing arithmetic sequence {ai}i=1100\{a_i\}_{i=1}^{100}{ai}i=1100 of positive integers such that a1+a4+a9+⋯+a100=1000,a_1+a_4+a_9+\cdots+a_…
- Find the sum of the first 75 terms of the arithmetic sequence 7,3,−1,−5,−9,…7,3,-1,-5,-9,\dots7,3,−1,−5,−9,…
- Convert the following recursive formula for g(n)g(n)g(n) to an explicit formula. g(0)=0g(0) = 0g(0)=0 g(1)=1g(1) = 1g(1)=1 g(n)=n+g(n−1)g(n) = n + g(n-1)g(n)=n+g(n−1)
- Find the positive value of nnn that satisfies 1+3+5+7+⋯+2011+2013+2015=n21 + 3 + 5 + 7 + \cdots + 2011 + 2013 + 2015 = n^21+3+5+7+⋯+2011+2013+2015=n2.
- What is the value of x1⋅x2⋅x3⋅ ... ⋅x10x^1 \cdot x^2 \cdot x^3 \cdot \text{ ... } \cdot x^{10}x1⋅x2⋅x3⋅ ... ⋅x10?
- Compute (1917+1918+⋯+2016)−(417+418+⋯+516)(1917 + 1918 + \cdots + 2016) - (417 + 418 + \cdots + 516)(1917+1918+⋯+2016)−(417+418+⋯+516).
- Compute 27+37+⋯+87\frac27 + \frac37 + \cdots + \frac8772+73+⋯+78.
- It's blueberry season! Every day, you eat five more blueberries than you did in the previous day. After the sixth day, you realize that you have eaten 117 blueberries. How many …
- What is the imaginary part of i1⋅i3⋅i5⋅i7⋅i9i^1\cdot i^3 \cdot i^5 \cdot i^7 \cdot i^9i1⋅i3⋅i5⋅i7⋅i9?
- If (5+9+13.......... n terms) 17 ___________________ = _ (7+9+11.........(n+1)terms 16 The value of n is
- Solve equation (A) and plug the result into expression (B). 100x+99x+98x+⋯+2x+x=10100(A)100−x(B)\begin{array}{lc} 100x+99x+98x+\dots+2x+x=10100&\quad\small{(A)}\\ 100-x&\quad\sm…