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. ...
T hat is, S=a1+an)Find the sum of the terms in the sequence 1,2,3,4,5,6,7,8,9,10.T he first term is i and the last of the 1o terms is 1, so the sum is(1+1)=5. 相关知识点: 试题来源: 解析 【解析】55. 反馈 收藏 ...
You might also find our sum of linear number sequence calculator interesting. How do I calculate the sum of a geometric series? To know how to find the sum of a series in geometric progression, we can use either the finite sum formula or the infinite sum calculation. A geometric series ...
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. ...
(summation notation )Derived from the18 th letter of the Greek alphabet,this symbol∑is used to represent the sum of all the values in an arithmetic sequence.signed number A number that is written with a plus sign a positive number or a minus sign (a negative number).Both+26 and-14 ...
Now substituting back into the equation for \(S_n\): \(S_n = \frac{1}{1 - x} \left( n + \sqrt{x} \cdot \frac{n^2 - 3n}{2} \right)\) Step 6: Final ExpressionThus, the final expression for the sum of the series to n terms is: \(S_n = \frac{1}{1 - x} \...
Therefore, the minimum sum of our infinite geometric sequence is (E)4. (Solution by akaashp11) As an extension to find the maximum value for the denominator we can find the derivative of −r2+r to get 1−2r. we know that this changes sign when r=12 so plugging it in into the ...
The sum of the first n natural numbers is given by the formula: n∑r=1r=n(n+1)2 Thus, substituting this into our equation gives: n∑r=1br=b⋅n(n+1)2 Step 3: Combine the results Now, we can combine both parts of the summation: n∑r=1(ar+br)=n∑r=1ar+n∑r=1br Subst...
Finally, add the last addend in the sequence to 10. Your final total is 18. 4. C is incorrect. How did we get here? Read the problem: Which of the following is incorrect? 3 + 4 = 7 10 + 18 = 28 7 + 6 = 12 4 + 16 = 20 For each problem, find the sum of the two ...