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
In an A.P., if pth term is 1/q and qth term is 1/p, prove that the sum of first pq terms is 1/2 (pq + 1) where `p != q`
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 `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)th numbers is 5:9. Find the value of m.
A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter 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.
A manufacturer reckons that the value of a machine, which costs him Rs 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.
A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.
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 = 2n + 7. Show that it is an A.P. Also, find its 7th term.
If the sequence < an > is an A.P., show that am +n +am − n = 2am.
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 sum of the following arithmetic progression :
1, 3, 5, 7, ... to 12 terms
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Find the sum of first n odd natural numbers.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
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.
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
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.
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 carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?
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.
If m th term of an A.P. is n and nth term is m, then write its pth term.
If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is
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
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
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 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 ______.
The first term of an A.P.is a, and the sum of the first p terms is zero, show that the sum of its next q terms is `(-a(p + q)q)/(p - 1)`
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
If the sum of n terms of a sequence is quadratic expression then it always represents an A.P
