हिंदी

If `A(1/B + 1/C), B(1/C+1/A), C(1/A+1/B)` Are in A.P., Prove That A, B, C Are in Arithmetic Progression

Advertisements
Advertisements

प्रश्न

if `a(1/b + 1/c), b(1/c+1/a), c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.

Advertisements

उत्तर

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.


Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.

Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`


Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.


Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

 3, −1, −5, −9 ...


Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case. 

9, 7, 5, 3, ...


Find:

nth term of the A.P. 13, 8, 3, −2, ...


Which term of the A.P. 3, 8, 13, ... is 248?


Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely real ?


The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.


If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.


Find the 12th term from the following arithmetic progression:

 3, 5, 7, 9, ... 201


Find the sum of the following arithmetic progression :

1, 3, 5, 7, ... to 12 terms


Find the sum of the following arithmetic progression :

3, 9/2, 6, 15/2, ... to 25 terms


Find the sum of the following arithmetic progression :

41, 36, 31, ... to 12 terms


Find the sum of first n odd natural numbers.


Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.


The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.


The number of terms of an A.P. is even; the sum of odd terms is 24, of the even terms is 30, and the last term exceeds the first by \[10 \frac{1}{2}\] , find the number of terms and the series. 


If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?


If the sum of a certain number of terms of the AP 25, 22, 19, ... is 116. Find the last term.


If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1 : S2 = (2n + 1) : (n + 1).


If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.


If a, b, c is in A.P., prove that:

a2 + c2 + 4ac = 2 (ab + bc + ca)


Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.


Write the sum of first n odd natural numbers.


Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.


If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.


If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is


In the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2 n terms to the next 2 nterms is


If abc are in G.P. and a1/b1/y = c1/z, then xyz are in


If there are (2n + 1) terms in an A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is (n + 1) : n


If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that `(m + n) (1/m - 1/p) = (m + p) (1/m - 1/n)`


If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad


In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.


A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?


If 100 times the 100th term of an A.P. with non zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×