If the sum of first n terms of an A.P. is cn2, then sum of squares of these n terms is?




2 years ago


Answers : (1)


If a is 1st term and d is common difference, sum of n terms = (n/2) (2a + (n-1)d) = (2an-nd) + n2d


comparing this with cn2 we get : 2an-nd = 0  and  d = c    =>    a = c/2,  d = c


sum of squares of n terms = \sum_{r=1}^{n}(a+(n-1)d)^{2}


=\sum_{r=1}^{n}\left( \frac{c}{2}+(n-1)c\right)^{2}


=\sum_{r=1}^{n}c^{2}\left( n^{2}-n+\frac{1}{4}\right)


=c^{2}\left( \sum_{r=1}^{n}n^{2}-\sum_{r=1}^{n}n+\sum_{r=1}^{n}\frac{1}{4}\right)





2 years ago

Post Your Answer

More Questions On Algebra

Ask Experts

Have any Question? Ask Experts
Post Question
Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details
if a 2 +b 2 +c 2 -ab-bc-ca=0 then show that a=b=c .
Hello student, Please find the answer to your question below a² + b² + c² = ab + bc + ca Multiplying both sides with "2", we have 2 ( a² + b² + c² ) =...
the number of words in SUCCESS in which the consonents appear in alphabetic order is? please give detail answer so that i can solve all alpabetic arrangement questions. thanks
Hello student, In the above answer i mentioned number of words having consonants in alphabetical order in the word SUCCESS and that is what you have asked also previously.please check your...
SHAIK AASIF AHAMED one month ago
Hello student, Please find the answer to your question below In any rearrangement of the word SUCCESS, there are 5!/3!2!=10 ways to permutate theconsonents in the word. Only 1 of out these...
i asked how many words are there before success in dictonary
vineet nimesh one month ago
A certain item is manufactured at two plants 1 and 2.Plant 1 make 70% of the requirement and plant 2 makes 30%.From plant 1, 90% meet a particular standard and plant 2 only 80% meet such...
Hi, Part a : 70 produced from plant one and 30 produced from plant 2. [70 * 0.9] + [30 * 0.8] = 87 Part 2 : Total standard product = 87 standard product from plant 2 = 24 Probability : 24/87...
Yash Baheti one month ago
Help …....image attached
Hello student, Please find answer to your question Differentiate Differentiate
Jitender Singh 3 months ago
what is the use of vector space
To represent the quantity wich have both magnitude and direction.
Vineeth one month ago
Hiiii I am from tutorsduniya.com .We connect students with teachers on facebook,whats app,etc.You can clear your concepts from teachers .You can ask them anything , you like to, be frank...
vikash khandelwal 25 days ago
By understanding laws of vectors we can represent a physical quantity wich has both magnitude and direction in mathematical form ,also with selecting a reference point . By understanding...
Vineeth one month ago
A tangent to the ellipse x 2 +y 2 =4 meets the ellipse x 2 +2y 2 =6 at P &Q.The angle b/w the tangents at P & Q of ellipse x 2 +2y 2 =6 is......
Please check the question and post it once again x 2 +y 2 =4 is not a eqn of ellipse...
Nishant Vora 21 days ago
View all Questions »