Before I show you how to find the sum of arithmetic series, you need to know what an arithmetic series is or how to recognize it.A series is an expression for the sum of the terms of a sequence. For example, 6 + 9 + 12 + 15 + 18 is a series for it is the expression for ...
Example 3: Using the sum of arithmetic sequence formula, calculate the sum of the first 20 terms of the sequence 1, 5, 9, 13, ……Solution:Here, a1 = 1, d = 4 and n = 20.Using the sum of arithmetic series formula,Sn=n2[2a1+(n−1)d]=202[2(1)+(20−1)4]=10×(2+...
2) sum of arithmetic series 等差数列求和3) sum of seguence 数列求和 1. Owing to position in the mathematics of few row at senior high school and developing student\'s logic reasons ability and the reasonableness thinking level mathematics teaching should strengthen the teaching of sum of ...
For example, 1+4+7+10+13+16 is an arithmetic series where the common difference is 3. The sum, s, of the arithmetic series a1+a2+⋯+an is given by the formula s=n(a1+an2) where n is the number of terms, a1 is the first term of the series, and an is last term...
What formula is used in arithmetic sequence? An arithmetic sequence refers to a series of numbers separated by a constant difference between adjacent terms. The formula used to solve the sum of an arithmetic sequence is: n/22a + (n-1)d, where n = the number of terms to be added, a ...
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 right-hand side of this equation comprises n terms, each of which is the sum of the first and last term. Writing the right-hand side as , 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 ...
英语翻译The sum of the first 5 terms of an arithmetic series is 85.The sum of the first 6 terms is 123.Determine the first four terms of the series. 答案 一个数学系列前5项之和是85,前六项之和是123,求前4项?1# X2# X+Y3# X+2Y4# X+3Y5# X+4Y6# X+5Y=38 (前5项之和是85...
4 The sum of the first n terms of an arithmetic series is 2n(n +3)Find(a) the first term of the series,2 ×4=8(1)(b)the common difference of the series,S_2=2a+d=4*5(3)d=4(c) the 25th term of the series.(2)25th term=a+24d=8+24 × 4=104 ...
The sum of the odd numbers (from 1) up to to 500 is 62500. The sum of an arithmetic series is given by: sum = 1/2 x number_in_series x (first + last) For the odd numbers from 1 to 500, there is: number_in_series = 250 first = 1 last = 499 which gives the sum as: ...