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Arithmetic Series: Formula & Equation Geometric Sequence | Definition, Formula & Examples Sum of Arithmetic Sequence | Formula & Examples Start today. Try it now Study.com ACT Study Guide and Test Prep 30 chapters | 159 lessons Ch 1. Study.com ACT® Test Prep: What to Expect on....
Writing the right-hand side as n(a_1+a_n), the equation becomes 2S=n(a_1+a_n), so the sum of the first n terms of the arithmetic series, S, is equal to one-half the number of terms multiplied by the sum of the first and last terms. That is, S= n2(a_1+a_n). Find ...
, the equation becomes , so the sum of the first n terms of the arithmetic series, S, is equal to one-half the number of terms multiplied by the sum of the first and last terms. That is, . Find the sum of the terms in the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. ...
【题目】A series is the sum of the terms in a sequence, so an arithmetic series is the sum of theterms in an arithmetic sequence. Let s represent the sum: S=a1+a2+a3+..+an-2+an-1.Write+anthe sum again, except write the terms from last term to first termS=an+an-1+an-2+....
The sum of the first 10terms of the sequence is 162.(a) Show that 10a+45 d =162Given also that the sixth term of the sequence is 17.(b) write down a secon d equation in a an d d,(c) fin d the value of a an d the value of d. ...
Arithmetic Sequence Formula Arithmetic Sequence Examples Lesson Summary Register to view this lesson Are you a student or a teacher? I am a student I am a teacher Recommended Lessons and Courses for You Related Lessons Related Courses Arithmetic Series: Formula & Equation Sum of Natural ...
Then, by adding the two arithmetic sequence, all terms involvingdwill be cancelled out. Thus, having the equation: $2S_n = n (a_1 + a_n)$ Dividing both sides of the equation by 2 will result to: $S_n = \frac{n (a_1 + a_n)}{2}$ ...
Note that Sn, and Tn, both being the sum of the first n terms of an arithmetic sequence, are both quadratic polynomials with constant term 0. Hence we may assume Sn=An2+Bn and Tn=Cn2+Dn. Consequently, an=Sn−Sn−1=2An+(B−A). Similarly bn=2Cn+(D−C). Plugging these...
Problem 14: In an arithmetic sequence an, if a_3a_7=-16 , a_4+a_6=0 , find Sn, the sum of first n terms. 相关知识点: 试题来源: 解析 Problem 14: Solution: n(n-9)or-n(n-9). Let the common difference of the arithmetic se- quence an be d \(a_1+2d=(a_1+6d)=...