Home
Class 12
MATHS
If a, b, c, d are in G.P, prove that (a...

If a, b, c, d are in G.P, prove that `(a^n + b^n), (b^n + c^n), (c^n + d^n)` are in G.P.

Text Solution

Verified by Experts

It is given that a,b,c and d are in G.P.
`thereforeb=ar,c=ar^(2),d=ar^(3)`
Now `(a^(n)+b^(n))=(a^(n)+(ar)^(n))=a^(n)(1+r^(n))`
`(b^(n)+c^(n))=((ar)^(n)+(ar^(2))^(n))=a^(n)r^(n)(1+r^(n))`
`(c^(n)+d^(n))=((ar^(2))^(n)+(ar^(3))^(n))=a^(n)r^(2n)(1+r^(n))`
clearly, `(b^(n)+c^(n))/(a^(n)+b^(n))=(c^(n)+d^(n))/(b^(n)+c^(n)=r^(n)`
Thus,`(a^(n)+b^(n)),(b^(n)+c^(n)),(c^(n)+d^(n))` are in G.P.
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.5|10 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.6|11 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.3|9 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

If a, b, c, d are in G.P., then (a + b + c + d)^(2) is equal to

If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-1),(c^3+d^3)^(-1) are also in G.P.

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c-c/a b. a/c+c/a c. b/q+q/b d. b/q-q/b

If a ,b ,a n dc are in G.P. then prove that 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

If a, b, c are in A.P., b, c, d are in G.P. and 1/c,1/d,1/e are in A.P. prove that a,c,e are in GP.

If a ,b, c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

If a , b ,a n dc are in G.P., then a+b ,2b ,a n db+c are in a. A.P b. G.P. c. H.P. d. none of these

If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove that x ,a n d4,z are in H.P.

If a ,b ,ca n dd are in H.P., then prove that (b+c+d)//a ,(c+d+a)//b ,(d+a+b)//c and (a+b+c)//d , are in A.P.