Advertisements
Advertisements
प्रश्न
Which term of the A.P. 84, 80, 76,... is 0?
Advertisements
उत्तर
84, 80, 76...
Here, we have:
a = 84
\[d = \left( 80 - 84 \right) = - 4\]
\[\text { Let }a_n = 0\]
\[ \Rightarrow a + (n - 1)d = 0\]
\[ \Rightarrow 84 + (n - 1)\left( - 4 \right) = 0\]
\[ \Rightarrow (n - 1)\left( - 4 \right) = - 84\]
\[ \Rightarrow (n - 1) = 21\]
\[ \Rightarrow n = 22\]
Hence, 0 is the 22nd term of the given A.P.
APPEARS IN
संबंधित प्रश्न
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
if `a(1/b + 1/c), b(1/c+1/a), c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.
A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
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.
Let < an > be a sequence defined by a1 = 3 and, an = 3an − 1 + 2, for all n > 1
Find the first four terms of the sequence.
Let < an > be a sequence. Write the first five term in the following:
a1 = a2 = 2, an = an − 1 − 1, n > 2
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
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.
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.
If < an > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].
\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]
\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]
Find the sum of all integers between 84 and 719, which are multiples of 5.
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.
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 Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
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?
Find the sum of odd integers from 1 to 2001.
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 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.
If a, b, c is in A.P., then show that:
a2 (b + c), b2 (c + a), c2 (a + b) are also in A.P.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
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?
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?
Write the common difference of an A.P. the sum of whose first n terms is
Write the sum of first n even natural numbers.
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 Sn denotes the sum of first n terms of an A.P. < an > such that
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
Find the sum of first 24 terms of the A.P. a1, a2, a3, ... if it is known that a1 + a5 + a10 + a15 + a20 + a24 = 225.
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.
Let 3, 6, 9, 12 ....... upto 78 terms and 5, 9, 13, 17 ...... upto 59 be two series. Then, the sum of the terms common to both the series is equal to ______.
The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is ______.
