Advertisements
Advertisements
Question
Write the common difference of an A.P. whose nth term is xn + y.
Advertisements
Solution
\[\text { We have }: \]
\[ a_n = xn + y\]
\[ \therefore a_1 = x + y\]
\[ a_2 = 2x + y\]
Common difference of an A.P., d = \[a_2 - a_1\]
\[\Rightarrow \left( 2x + y \right) - \left( x + y \right)\]
\[ \Rightarrow x\]
APPEARS IN
RELATED QUESTIONS
The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nthterm is (2m – 1): (2n – 1)
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.
Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
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. Write the first five term in the following:
a1 = a2 = 2, an = an − 1 − 1, n > 2
The Fibonacci sequence is defined by a1 = 1 = a2, an = an − 1 + an − 2 for n > 2
Find `(""^an +1)/(""^an")` for n = 1, 2, 3, 4, 5.
Find:
18th term of the A.P.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]
Find:
nth term of the A.P. 13, 8, 3, −2, ...
Is 302 a term of the A.P. 3, 8, 13, ...?
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
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.
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of the series:
3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + ... to 3n terms.
Find the sum of n terms of the A.P. whose kth terms is 5k + 1.
Find an A.P. in which the sum of any number of terms is always three times the squared number of these 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:
(a − c)2 = 4 (a − b) (b − c)
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.
A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
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 Sn denotes the sum of first n terms of an A.P. < an > such that
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
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:
\[\text { If in an A . P } . S_n = n^2 q \text { and } S_m = m^2 q, \text { where } S_r \text{ denotes the sum of r terms of the A . P . , then }S_q \text { equals }\]
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 ______.
Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
