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 ______.
विकल्प
– 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
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.
Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.
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.
Which term of the A.P. 3, 8, 13, ... is 248?
Which term of the A.P. 84, 80, 76, ... is 0?
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progression :
41, 36, 31, ... to 12 terms
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
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 S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1 : S2 = (2n + 1) : (n + 1).
The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P.
If \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
bc, ca, ab are in A.P.
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 man saved Rs 16500 in ten years. In each year after the first he saved Rs 100 more than he did in the receding year. How much did he save in the first year?
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much the tractor cost him?
Write the common difference of an A.P. the sum of whose first n terms is
Write the sum of first n odd natural numbers.
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
If the sum of n terms of an A.P. be 3 n2 − n and its common difference is 6, then its first term is
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − k Sn − 1 + Sn − 2 , then k =
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
If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.
A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is ______.
