मराठी

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) - Mathematics

Advertisements
Advertisements

प्रश्न

The ratio of the sums of m and n terms of an A.P. is m2n2. Show that the ratio of mth and nthterm is (2m – 1): (2n – 1)

उत्तर

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

According to the given condition,

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Sequences and Series - Exercise 9.2 [पृष्ठ १८५]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 9 Sequences and Series
Exercise 9.2 | Q 12 | पृष्ठ १८५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the sum of odd integers from 1 to 2001.


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


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`


Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)


A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.


A manufacturer reckons that the value of a machine, which costs him Rs 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.


The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.


Find: 

18th term of the A.P.

\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]


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


How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\] 


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.


Find the 12th term from the following arithmetic progression:

1, 4, 7, 10, ..., 88


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.


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 arithmetic progression :

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


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


Find the sum of all integers between 50 and 500 which are divisible by 7.


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. 


The income of a person is Rs 300,000 in the first year and he receives an increase of Rs 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.


Write the common difference of an A.P. whose nth term is xn + y.


Write the sum of first n odd natural numbers.


If Sn denotes the sum of first n terms of an A.P. < an > such that

\[\frac{S_m}{S_n} = \frac{m^2}{n^2}, \text { then }\frac{a_m}{a_n} =\]

The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be


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


If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are


If n arithmetic means are inserted between 1 and 31 such that the ratio of the first mean and nth mean is 3 : 29, then the value of n is


If, S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2}\] = 


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


If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.


The pth term of an A.P. is a and qth term is b. Prove that the sum of its (p + q) terms is `(p + q)/2[a + b + (a - b)/(p - q)]`.


Find the sum of first 24 terms of the A.P. a1, a2, a3, ... if it is known that a1 + a5 + a10 + a15 + a20 + a24 = 225.


Show that (x2 + xy + y2), (z2 + xz + x2) and (y2 + yz + z2) are consecutive terms of an A.P., if x, y and z are in A.P.


If in an A.P., Sn = qn2 and Sm = qm2, where Sr denotes the sum of r terms of the A.P., then Sq equals ______.


If the sum of n terms of a sequence is quadratic expression then it always represents an A.P


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.