Advertisements
Advertisements
प्रश्न
If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.
Advertisements
उत्तर
\[\text { Let the three numbers be } (a - d), a, (a + d) . \]
\[\text { Sum } = 24\]
\[ \Rightarrow (a - d) + a + (a + d) = 24\]
\[ \Rightarrow 3a = 24\]
\[ \Rightarrow a = 8 . . . (i)\]
\[\text { Product } = a(a - d)(a + d) = 440\]
\[ \Rightarrow a( a^2 - d^2 ) = 440\]
\[ \Rightarrow 8(64 - d^2 ) = 440 \left(\text { Form } (i) \right)\]
\[ \Rightarrow (64 - d^2 ) = 55\]
\[ \Rightarrow d^2 = 9\]
\[ \Rightarrow d = \pm 3\]
\[\text { With a = 8, d = 3, we have }: \]
\[5, 8, 11\]
\[\text { With a = 8, d = - 3, we have: } \]
\[11, 8, 5\]
APPEARS IN
संबंधित प्रश्न
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
if `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.
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 integers from 1 to 100 that are divisible by 2 or 5.
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.
Let < an > be a sequence. Write the first five term in the following:
a1 = 1 = a2, an = an − 1 + an − 2, n > 2
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
Which term of the A.P. 4, 9, 14, ... is 254?
Find the 12th term from the following arithmetic progression:
1, 4, 7, 10, ..., 88
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
How many numbers of two digit are divisible by 3?
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of the following arithmetic progression :
(x − y)2, (x2 + y2), (x + y)2, ... to n 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 integers between 50 and 500 which are divisible by 7.
Find the sum of all even integers between 101 and 999.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
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.
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 \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
bc, ca, ab are in A.P.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
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.
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much the tractor cost him?
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
We know that the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.
Write the sum of first n odd natural numbers.
In the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2 n terms to the next 2 nterms is
If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [sec a1 sec a2 + sec a2 sec a3 + .... + sec an − 1 sec an], is
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
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.
If a, b, c are in G.P. and a1/x = b1/y = c1/z, then xyz are in
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
If n AM's are inserted between 1 and 31 and ratio of 7th and (n – 1)th A.M. is 5:9, then n equals ______.
If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is ______.
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 ______.
