Advertisements
Advertisements
Question
Which term of the A.P. 84, 80, 76,... is 0?
Advertisements
Solution
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
RELATED QUESTIONS
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
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.
Find the sum of all numbers between 200 and 400 which are divisible by 7.
The pth, qth and rth terms of an A.P. are a, b, c respectively. Show that (q – r )a + (r – p )b + (p – q )c = 0
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 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.
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 nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
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.
Find the sum of the following arithmetic progression :
41, 36, 31, ... to 12 terms
Find the sum of the following arithmetic progression :
\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.
Find the sum of the following serie:
101 + 99 + 97 + ... + 47
Find the sum of first n odd natural numbers.
Find the sum of all integers between 100 and 550, which are divisible by 9.
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
Find the sum of n terms of the A.P. whose kth terms is 5k + 1.
Find the sum of odd integers from 1 to 2001.
If a, b, c is in A.P., then show that:
bc − a2, ca − b2, ab − c2 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.
If \[a\left( \frac{1}{b} + \frac{1}{c} \right), b\left( \frac{1}{c} + \frac{1}{a} \right), c\left( \frac{1}{a} + \frac{1}{b} \right)\] are in A.P., prove that a, b, c are in A.P.
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.
In the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2 n terms to the next 2 nterms is
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
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
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
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
Show that (x2 + xy + y2), (z2 + xz + x2) and (y2 + yz + z2) are consecutive terms of an A.P., if x, y and z are in A.P.
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
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 b2, a2, c2 are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______
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 ______.
