Advertisements
Advertisements
प्रश्न
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Advertisements
उत्तर
\[\text { Let the three numbers be } a - d, a, a + d . \]
\[\text {Their sum } = 27\]
\[ \Rightarrow a - d + a + a + d = 27\]
\[ \Rightarrow 3a = 27\]
\[ \Rightarrow a = 9 . . . (i)\]
\[\text { Product } = (a - d)a(a + d) = 648\]
\[ \Rightarrow a( a^2 - d^2 ) = 648\]
\[ \Rightarrow 9(81 - d^2 ) = 648\]
\[ \Rightarrow (81 - d^2 ) = 72\]
\[ \Rightarrow d^2 = 9\]
\[ \Rightarrow d = \pm 3\]
\[\text { When a = 9, d = 3, we have:} \]
\[6, 9, 12\]
\[\text { When a = 9, d = - 3, we have: } \]
\[12, 9, 6\]
APPEARS IN
संबंधित प्रश्न
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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 defined by a1 = 3 and, an = 3an − 1 + 2, for all n > 1
Find the first four terms of the sequence.
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.
Find:
10th term of the A.P. 1, 4, 7, 10, ...
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th 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.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
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?
\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]
\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of first n odd natural numbers.
Find the sum of all integers between 50 and 500 which are divisible by 7.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
Find the sum of odd integers from 1 to 2001.
The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th 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 \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
\[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
A man saved Rs 16500 in ten years. In each year after the first he saved Rs 100 more than he did in the receding year. How much did he save in the first year?
A man starts repaying a loan as first instalment of Rs 100 = 00. If he increases the instalments by Rs 5 every month, what amount he will pay in the 30th instalment?
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?
Write the sum of first n odd natural numbers.
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
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 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 the first, second and last term of an A.P are a, b and 2a respectively, then its sum is
Mark the correct alternative in the following question:
\[\text { If in an A . P } . S_n = n^2 q \text { and } S_m = m^2 q, \text { where } S_r \text{ denotes the sum of r terms of the A . P . , then }S_q \text { equals }\]
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
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 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)`
Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.
The number of terms in an A.P. is even; the sum of the odd terms in lt is 24 and that the even terms is 30. If the last term exceeds the first term by `10 1/2`, then the number of terms in the A.P. is ______.
