English

If `(A^N + B^N)/(A^(N-1) + B^(N-1))` is the Arithmetic Mean Between a and B, Then Find the Value of N. - Mathematics

Advertisements
Advertisements

Question

if `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.

Solution

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Sequences and Series - Exercise 9.2 [Page 185]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 9 Sequences and Series
Exercise 9.2 | Q 15 | Page 185

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

How many terms of the A.P.  -6 , `-11/2` , -5... are needed to give the sum –25?


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


Find the sum to n terms of the A.P., whose kth term is 5k + 1.


If the sum of n terms of an A.P. is (pn qn2), where p and q are constants, find the common difference.


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


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.


Let < an > be a sequence. Write the first five term in the following:

a1 = 1 = a2, an = an − 1 + an − 2, n > 2


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, ...


Is 68 a term of the A.P. 7, 10, 13, ...?


How many terms are there in the A.P. 7, 10, 13, ... 43 ?


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


If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.


An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.


If < an > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].


Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.


The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.


Find the sum of the following arithmetic progression :

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


Find the sum of first n natural numbers.


Find the sum of all odd numbers between 100 and 200.


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


The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.


If 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?


If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:

\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P.


If a, b, c is in A.P., then show that:

b + c − a, c + a − b, a + b − c are in A.P.


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


A manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the total product in 7 years and (iii) the product in the 10th year.


Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.


Write the sum of first n odd natural numbers.


If the sum of n terms of an A.P. be 3 n2 − n and its common difference is 6, then its first term is


Sum of all two digit numbers which when divided by 4 yield unity as remainder is


If in an A.P., Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to


Mark the correct alternative in the following question:
If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term is


Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively. 


The first three of four given numbers are in G.P. and their last three are in A.P. with common difference 6. If first and fourth numbers are equal, then the first number is 


The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers


Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.


If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.


The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×