Advertisements
Advertisements
प्रश्न
Write the common difference of an A.P. whose nth term is xn + y.
उत्तर
\[\text { We have }: \]
\[ a_n = xn + y\]
\[ \therefore a_1 = x + y\]
\[ a_2 = 2x + y\]
Common difference of an A.P., d = \[a_2 - a_1\]
\[\Rightarrow \left( 2x + y \right) - \left( x + y \right)\]
\[ \Rightarrow x\]
APPEARS IN
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
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.
How many terms of the A.P. -6 , `-11/2` , -5... are needed to give the sum –25?
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 the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
if `a(1/b + 1/c), b(1/c+1/a), c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
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.
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
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.
If < an > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].
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 :
\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.
Find the sum of first n natural numbers.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of all even integers between 101 and 999.
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the sum of the series:
3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + ... to 3n terms.
The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.
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.
If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.
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.
If a, b, c is in A.P., then show that:
bc − a2, ca − b2, ab − c2 are in A.P.
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.
In a potato race 20 potatoes are placed in a line at intervals of 4 meters with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
Write the common difference of an A.P. the sum of whose first n terms is
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.
Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.
If m th term of an A.P. is n and nth term is m, then write its pth term.
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 product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
Show that (x2 + xy + y2), (z2 + xz + x2) and (y2 + yz + z2) are consecutive terms of an A.P., if x, y and z are in A.P.
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
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 the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
