Advertisements
Advertisements
Question
If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.
Advertisements
Solution
\[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }} = 7\]
\[ \Rightarrow \frac{\frac{n}{2}\left\{ 2 \times 3 + \left( n - 1 \right)2 \right\}}{\frac{10}{2}\left\{ 2 \times 5 + \left( 10 - 1 \right)3 \right\}} = 7\]
\[ \Rightarrow \frac{n\left( 4 + 2n \right)}{370} = 7\]
\[ \Rightarrow n^2 + 2n - 1295 = 0\]
\[ \Rightarrow n^2 + 37n - 35n - 1295 = 0\]
\[ \Rightarrow \left( n + 37 \right)\left( n - 35 \right)\]
\[ \Rightarrow n = 35, n = - 37\]
\[\text { Rejecting the negative value, we get }: \]
\[ \Rightarrow n = 35\]
APPEARS IN
RELATED QUESTIONS
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms
Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
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 ...
Is 68 a term of the A.P. 7, 10, 13, ...?
Find the sum of the following arithmetic progression :
\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
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.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
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.
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.
Find the sum of odd integers from 1 to 2001.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are in A.P.
If a, b, c is in A.P., prove that:
a3 + c3 + 6abc = 8b3.
If \[a\left( \frac{1}{b} + \frac{1}{c} \right), b\left( \frac{1}{c} + \frac{1}{a} \right), c\left( \frac{1}{a} + \frac{1}{b} \right)\] are in A.P., prove that a, b, c are in A.P.
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.
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 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.
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
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 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
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:
\[\text { If in an A . P } . S_n = n^2 q \text { and } S_m = m^2 q, \text { where } S_r \text{ denotes the sum of r terms of the A . P . , then }S_q \text { equals }\]
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.
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that `(m + n) (1/m - 1/p) = (m + p) (1/m - 1/n)`
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
The first term of an A.P.is a, and the sum of the first p terms is zero, show that the sum of its next q terms is `(-a(p + q)q)/(p - 1)`
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
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 ______.
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
