English

The Ratio of the Sums of M and N Terms of an A.P. is M2: N2. Show that the Ratio of Mth and Nth Term is (2m – 1): (2n – 1)

Advertisements
Advertisements

Question

The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nthterm is (2m – 1): (2n – 1)

Advertisements

Solution

Let a and b be the first term and the common difference of the A.P. respectively.

According to the given condition,

shaalaa.com
  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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.


A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.


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

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


The Fibonacci sequence is defined by a1 = 1 = a2, an = an − 1 + an − 2 for n > 2

Find `(""^an +1)/(""^an")` for n = 1, 2, 3, 4, 5.

 


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 ...


The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.


Which term of the A.P. 4, 9, 14, ... is 254?


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 (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.


If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.


The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.


How many numbers of two digit are divisible by 3?


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


How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?


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


Find the sum of the following serie:

101 + 99 + 97 + ... + 47


Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.


Find the sum of all integers between 84 and 719, which are multiples of 5.


Find the sum of all even integers between 101 and 999.


Find the sum of the series:
3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + ... to 3n terms.


There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.


A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much the tractor cost him?


A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.


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


If log 2, log (2x − 1) and log (2x + 3) are in A.P., write the value of x.


If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be


In n A.M.'s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3 : 1, then the value of n is


Mark the correct alternative in the following question:

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


If second, third and sixth terms of an A.P. are consecutive terms of a G.P., write the common ratio of the G.P. 


The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is `((b + c - 2a)(c + a))/(2(b - a))`.


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


A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earnings during the first year?


If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.


If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is ______.


The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.


If b2, a2, c2 are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×