Advertisements
Advertisements
प्रश्न
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
पर्याय
\[-\]p
p
p + q
p-q
Advertisements
उत्तर
\[\text { As, } a_p = q\]
\[ \Rightarrow a + \left( p - 1 \right)d = q . . . . . \left( i \right)\]
\[\text { Also }, a_\left( p + q \right) = 0\]
\[ \Rightarrow a + \left( p + q - 1 \right)d = 0 . . . . . \left( ii \right)\]
\[\text { Subtracting } \left( i \right) \text { from } \left( ii \right), \text { we get }\]
\[a + \left( p + q - 1 \right)d - a - \left( p - 1 \right)d = 0 - q\]
\[ \Rightarrow \left( p + q - 1 - p + 1 \right)d = - q\]
\[ \Rightarrow qd = - q\]
\[ \Rightarrow d = \frac{- q}{q}\]
\[ \Rightarrow d = - 1\]
\[\text { Substituting } d = - 1 \text { in } \left( i \right), \text { we get }\]
\[a + \left( p - 1 \right) \times \left( - 1 \right) = q\]
\[ \Rightarrow a - p + 1 = q\]
\[ \Rightarrow a = p + q - 1\]
\[\text { Now }, \]
\[ a_q = a + \left( q - 1 \right)d\]
\[ = p + q - 1 + \left( q - 1 \right) \times \left( - 1 \right)\]
\[ = p + q - 1 - q + 1\]
\[ = p\]
Hence, the correct alternative is option (b).
APPEARS IN
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
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 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.
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 = 2n2 + n + 1. Show that it is not an A.P.
Which term of the A.P. 3, 8, 13, ... is 248?
Which term of the A.P. 4, 9, 14, ... is 254?
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 the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.
Find the sum of first n natural numbers.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
If 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
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).
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:
a3 + c3 + 6abc = 8b3.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
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?
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?
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?
A man accepts a position with an initial salary of ₹5200 per month. It is understood that he will receive an automatic increase of ₹320 in the very next month and each month thereafter.
(i) Find his salary for the tenth month.
(ii) What is his total earnings during the first year?
Write the sum of first n odd natural numbers.
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 3 n2 + 5 n then which of its terms is 164?
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.
If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that `(m + n) (1/m - 1/p) = (m + p) (1/m - 1/n)`
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)`
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
