English

The Sums of N Terms of Two Arithmetic Progressions Are in the Ratio 5n + 4: 9n + 6. Find the Ratio of Their 18th Terms

Advertisements
Advertisements

Question

The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms

Advertisements

Solution

Let a1a2, and d1dbe the first terms and the common difference of the first and second arithmetic progression respectively.

According to the given condition,

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

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


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


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


A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.


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

a1 = a2 = 2, an = a− 1 − 1, n > 2


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


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


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


Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.


The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.


Find the sum of the following arithmetic progression :

50, 46, 42, ... to 10 terms


Find the sum of the following arithmetic progression :

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


Find the sum of the following serie:

(a − b)2 + (a2 + b2) + (a + b)2 + ... + [(a + b)2 + 6ab]


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


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


Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.


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.


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?


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


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 a, b, c is in A.P., prove that:

 a3 + c3 + 6abc = 8b3.


A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.


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.


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.


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


If the sum of n terms of an AP is 2n2 + 3n, then write its nth term.


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


If m th term of an A.P. is n and nth term is m, then write its pth term.


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


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


Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − k Sn − 1 + Sn − 2 , then k =


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


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


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


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?


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. Find his salary for the tenth month


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×