If a(a), a (2), a (3),…., a(n) are in H....

If `a_(a), a _(2), a _(3),…., a_(n)` are in H.P. and `f (k)=sum _(r =1) ^(n) a_(r)-a_(k) ` then `(a_(1))/(f(1)), (a_(2))/(f (2)), (a_(3))/(f (n))` are in :

A.P.

G.P.

H.P.

none

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

PROGRESSIONS
ML KHANNA|Exercise PROBLEM SET - 5 (Assertion/Reason) |1 Videos
PROGRESSIONS
ML KHANNA|Exercise PROBLEM SET - 5 (TRUE AND FALSE) |5 Videos
PROGRESSIONS
ML KHANNA|Exercise PROBLEM SET - 4 (FILL IN THE BLANKS) |7 Videos
PROBABILITY
ML KHANNA|Exercise MISCELLANEOUS EXERCISE|6 Videos
PROPERTIES OF TRIANGLES
ML KHANNA|Exercise Self Assessment Test (Multiple Choise Questions)|34 Videos

Similar Questions

Explore conceptually related problems

If a_(1),a_(2),a_(3),...a_(n) are in H.P.and f(k)=(sum_(r=1)^(n)a_(r))-a_(k), then (a_(1))/(f(1)),(a_(2))/(f(2)),(a_(3))/(f(3)),...(a_(n))/(f(n)), are in a.A.P b.G.P. C.H.P.d.none of these

If a_(1),a_(2),".....", are in HP and f_(k)=sum_(r=1)^(n)a_(r)-a_(k) , then 2^(alpha_(1)),2^(alpha_(2)),2^(alpha_(3))2^(alpha_(4)),"....." are in {" where " alpha_(1)=(a_(1))/(f_(1)),alpha_(2)=(a_(2))/(f_(2)),alpha_(3)=(a_(3))/(f_(3)),"....."} .

If a_(1),a_(2),a_(3),a_(4) are in HP, then (1)/(a_(1)a_(4))sum_(r=1)^(3)a_(r)a_(r+1) is root of :

If a_(1),a_(2),a_(3)...a_(2n-1) are in H.P.then sum_(k=1)^(2n)(-1)^(k)(a_(k)+a_(k+1))/(a_(k)-a_(k+1)) is equal to

if a,A_(1),A_(2),A_(3)......,A_(2n),b are in A.P.then sum_(i=1)^(2n)A_(i)=(a+b)

a_(1),a_(2),a_(3)...,a_(n) are in A.P.such that a_(1)+a_(3)+a_(5)=-12 and a_(1)a_(2)a_(3)=8 then:

If a_(1),a_(2),a_(3),...,a_(2n+1) are in A.P.then (a_(2n+1)-a_(1))/(a_(2n+1)+a_(1))+(a_(2n)-a_(2))/(a_(2n)+a_(2))+...+(a_(n+2)-a_(n))/(a_(n+2)+a_(n)) is equal to (n(n+1))/(2)xx(a_(2)-a_(1))/(a_(n+1)) b.(n(n+1))/(2) c.(n+1)(a_(2)-a_(1)) d.none of these

a_(1),a_(2),a_(3),......,a_(n), are in A.P such that a_(1)+a_(3)+a_(5)=-12 and a_(1)a_(2)a_(3)=8 then

ML KHANNA-PROGRESSIONS -PROBLEM SET - 5 (MULTIPLE CHOICE QUESTIONS)

(i) The value of x + y + z is 15. If a, x, y, z, b are in AP while the...
Text Solution
|
If a,b,c,d are in H.P., then ab+bc+cd is equal to
Text Solution
|
If a(a), a (2), a (3),…., a(n) are in H.P. and f (k)=sum (r =1) ^(n) a...
Text Solution
|
If A, G & H are respectively te A.M., G.M. & H.M. of three positive nu...
Text Solution
|
In an H.P., T(p) = q (p + q), T(q) = p (p + q), then p and q are the r...
Text Solution
|
If four positive numbers a, b, c, d are in H.P. then which one of the ...
Text Solution
|
The A.M., G.M. and H.M. between two positive numbers a and b are equal...
Text Solution
|
The AM, HM and GM between two numbers are (144)/(15), 15 and 12, but n...
Text Solution
|
If 2(y-a) is the harmonic mean between y-x and y-z then x-a, y—a and z...
Text Solution
|
IF a(1),a(2),a(3),"...."a(10) be in AP and h(1),h(2),h(3),"...."h(10) ...
Text Solution
|
If a(1), a(2), a(3) and h(1), h(2), h(3) are the A.M.'s and H.M.'s bet...
Text Solution
|
If H(1), H(2),…., H(n) be n harmonic means between a and b then (H(1) ...
Text Solution
|
If n is a root of the equation (1 - ab) x^(2) - (a^(2) + b^(2)) x - (1...
Text Solution
|
If (1)/(b+c) , (1)/(c+a) and (1)/(a+b) are in AP, then a^(2), b^(2) an...
Text Solution
|
If three numbers are in G.P., then the numbers obtained by adding the ...
Text Solution
|
If three numbers are in H.P., then the numbers obtained by subtracting...
Text Solution
|
If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-...
Text Solution
|
If a, b, c, d be four numbers of which the first three are in AP and t...
Text Solution
|
If S(k) denotes the sum of first k terms of a G.P. Then, S(n),S(2n)-S(...
Text Solution
|
If x, y, z be in A.P., then x + (1)/(yz), y + (1)/(zx), z + (1)/(xy) a...
Text Solution
|