Home
Class 12
MATHS
Let a (1) , a (2), ….a (2n) be an arithm...

Let `a _(1) , a _(2), ….a _(2n)` be an arithmetic progression of positive real numbers with common difference d. Let
(i) `a _(1) ^(2) + a _(3) ^(2) +…..+ a _(2n -1) ^(2) = x,`
(ii) `a _(2) ^(2 ) + a _(4) ^(2) +….+ a _(2n) ^(2) =y,` and
(iii)` a _(n) + a _(n +1) = z.`
Express d in terms of x,y,z,n.

Text Solution

Verified by Experts

The correct Answer is:
`d = (y -x)/(zn)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    RESONANCE|Exercise EXERCISE -2 (PART -I PREVIOUS ASKED QUESTION FOR PRE RMO)|18 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise SSP|55 Videos

  • TEST PAPER

    RESONANCE|Exercise CHEMISTRY|37 Videos

Similar Questions

Explore conceptually related problems

If the sum of 'n' terms of an arithmetic progression is S_(n)=3n +2n^(2) then its common difference is :

Let a_n , n ge 1 , be an arithmetic progression with first term 2 and common difference 4. Let M_n be the average of the first n terms. Then the sum_(n=1)^10 M_n is

If S_(n)=n^(2)a+(n)/(4)(n-1)d is the sum of the first n terms of an arithmetic progression, then the common difference is

Lim {x rarr oo} {(1+ (1) / (n ^ (2))) ^ ((2) / (n ^ (2))) (1+ (4) / (n ^ (2)) ) ^ ((4) / (n ^ (2))) ...... (1+ (n ^ (2)) / (n ^ (2))) ^ (2 (n) / (n ^ (2)))}

Let (1+x^2^2)^2(1+x)^n = sum _(k=0)^(n+4)a_k x^k. If a_1,a_2,a_3 are in rithmetic progression find n.

Assign the position of the element having outer electronic configuration : (i) ns^(2) np ^(4) for n =3 (ii) (n-1)d ^(2) ns ^(2) for n =4 (iii) (n -2) f ^(7) (n -1) d ^(1) ns ^(2) for n =6 in the periodic table.

Let n be a positive integer and (1+x+x^(2))^(n)=a_(0)+a_(1)x+...+a^(2n)x^(2n) Show that a_(0)^(2)-a_(1)^(2)+a_(2)^(2)+...+a_(2n)^(2)=a_(n)

For any positive real number a and for any n in N , the greatest value of (a^(n))/(1+a+a^(2)+…+a^(2n)) , is

Assign the position of the element having outer electronic configuration (i) ns^(2) np^(2) for n = 2 (ii) (n-1) d^(5) ns^(1) for n = 4 , and (iii) (n-2) f^(14) (n-1) d^(0) ns^(2) for n = 6 in the Modern periodic table.