हिंदी

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

प्रश्न

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

उत्तर

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


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`


Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.


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?


If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.


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


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


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.


In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.


Find the 12th term from the following arithmetic progression:

 3, 5, 7, 9, ... 201


How many numbers of two digit are divisible by 3?


The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.


Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.


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


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


Find the sum of all integers between 100 and 550, which are divisible by 9.


Solve: 

1 + 4 + 7 + 10 + ... + x = 590.


If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.


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


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.


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 a2, b2, c2 are in A.P., prove that \[\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}\] are in 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.


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.


In a cricket team tournament 16 teams participated. A sum of ₹8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?


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 the sums of n terms of two arithmetic progressions are in the ratio 2n + 5 : 3n + 4, then write the ratio of their m th terms.


If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [cosec a1cosec a2 + cosec a1 cosec a3 + .... + cosec an − 1 cosec an] 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 =


The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] ,  then k =


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


If abc are in A.P. and xyz are in G.P., then the value of xb − c yc − a za − b is


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


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.


Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.


Let 3, 6, 9, 12 ....... upto 78 terms and 5, 9, 13, 17 ...... upto 59 be two series. Then, the sum of the terms common to both the series is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×