Advertisements
Advertisements
प्रश्न
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
पर्याय
– p
p
p + q
p – q
Advertisements
उत्तर
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is p.
Explanation:
Let a, d be the first term and common difference respectively.
Therefore, Tp = a + (p – 1)d = q ......(1)
Tp+ q = a + (p + q – 1)d = 0 .....(2)
Subtracting (1), from (2) we get qd = – q
Substituting in (1) we get
a = q – (p – 1)(–1) = q + p – 1
Now Tq = a + (q – 1)d = q + p – 1 + (q – 1)(–1)
= q + p – 1 – q + 1
= p
APPEARS IN
संबंधित प्रश्न
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.
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
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 ...
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
Which term of the sequence 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th 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.
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
Find the 12th term from the following arithmetic progression:
3, 5, 7, 9, ... 201
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
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.
The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.
If the sum of three numbers in A.P. is 24 and their product is 440, find the 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 those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
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 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
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.
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, b, c is in A.P., then show that:
bc − a2, ca − b2, ab − c2 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 starts repaying a loan as first instalment of Rs 100 = 00. If he increases the instalments by Rs 5 every month, what amount he will pay in the 30th instalment?
We know that the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.
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?
If the sum of n terms of an AP is 2n2 + 3n, then write its nth term.
If Sn denotes the sum of first n terms of an A.P. < an > such that
If n arithmetic means are inserted between 1 and 31 such that the ratio of the first mean and nth mean is 3 : 29, then the value of n is
If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is
If, S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2}\] =
Mark the correct alternative in the following question:
If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term 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 second, third and sixth terms of an A.P. are consecutive terms of a G.P., write the common ratio of the G.P.
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 rth term of an A.P. sum of whose first n terms is 2n + 3n2
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
If n AM's are inserted between 1 and 31 and ratio of 7th and (n – 1)th A.M. is 5:9, then n equals ______.
The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.
