Advertisements
Advertisements
प्रश्न
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
पर्याय
5, 10, 15, 20
4, 10, 16, 22
3, 7, 11, 15
none of these
Advertisements
उत्तर
5, 10, 15, 20
Let the four numbers in A.P. be as follows:
\[a - 2d, a - d, a, a + d\]
Their sum = 50 (Given)
\[\Rightarrow \left( a - 2d \right) + \left( a - d \right) + a + \left( a + d \right) = 50\]
\[ \Rightarrow 2a - d = 25 . . . . . \left( 1 \right)\]
\[\text { Also }, \left( a + d \right) = 4\left( a - 2d \right)\]
\[ \Rightarrow a + d = 4a - 8d\]
\[ \Rightarrow 3d = a . . . . . . \left( 2 \right)\]
From equations \[\left( 1 \right) \text { and }\left( 2 \right),\] , we get:
d = 5, a = 15
Hence, the numbers are
\[15 - 10, 15 - 5, 15, 15 + 5\], i.e. 5, 10, 15, 20.
APPEARS IN
संबंधित प्रश्न
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms
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?
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
Let < an > be a sequence. Write the first five term in the following:
a1 = a2 = 2, an = an − 1 − 1, n > 2
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, ...?
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.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.
Find the sum of the following arithmetic progression :
1, 3, 5, 7, ... to 12 terms
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
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 first n natural numbers.
Find the sum of all odd numbers between 100 and 200.
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
If a, b, c is in A.P., prove that:
a2 + c2 + 4ac = 2 (ab + bc + ca)
Show that x2 + xy + y2, z2 + zx + x2 and y2 + yz + z2 are consecutive terms of an A.P., if x, y and z are in A.P.
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 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?
Write the sum of first n even 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
If Sn denotes the sum of first n terms of an A.P. < an > such that
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 3 n2 + 5 n then which of its terms is 164?
If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is
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 =
Mark the correct alternative in the following question:
Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
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
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.
If a1, a2, ..., an are in A.P. with common difference d (where d ≠ 0); then the sum of the series sin d (cosec a1 cosec a2 + cosec a2 cosec a3 + ...+ cosec an–1 cosec an) is equal to cot a1 – cot an
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?
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
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 ______.
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 ______.
