Advertisements
Advertisements
प्रश्न
If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.
उत्तर
APPEARS IN
संबंधित प्रश्न
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
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 `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.
If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.
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 ...
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
−1, 1/4, 3/2, 11/4, ...
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
Find:
18th term of the A.P.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]
Is 68 a term of the A.P. 7, 10, 13, ...?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Find the 12th term from the following arithmetic progression:
1, 4, 7, 10, ..., 88
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.
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 are there between 1 and 1000 which when divided by 7 leave remainder 4?
\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]
\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]
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 the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of all integers between 50 and 500 which are divisible by 7.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
Find an A.P. in which the sum of any number of terms is always three times the squared number of these terms.
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 x, y, z are in A.P. and A1 is the A.M. of x and y and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.
A man saved ₹66000 in 20 years. In each succeeding year after the first year he saved ₹200 more than what he saved in the previous year. How much did he save in the first year?
Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
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
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:
The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is
If second, third and sixth terms of an A.P. are consecutive terms of a G.P., write the common ratio of the G.P.
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. Find his salary for the tenth month
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
If the sum of n terms of a sequence is quadratic expression then it always represents an A.P
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
