Advertisements
Advertisements
प्रश्न
Find:
18th term of the A.P.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]
Advertisements
उत्तर
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}\]......
We have:
\[a = \sqrt{2}\]
\[d = 3\sqrt{2} - \sqrt{2} = 2\sqrt{2}\]
\[a_{18} = a + \left( 18 - 1 \right)d \left[ a_n = a + \left( n - 1 \right)d \right] \]
\[ = a + 17d\]
\[ = \sqrt{2} + 17\left( 2\sqrt{2} \right)\]
\[ = \sqrt{2} + 34\sqrt{2}\]
\[ = 35 \sqrt{2}\]
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.
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.
The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.
Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
The Fibonacci sequence is defined by a1 = 1 = a2, an = an − 1 + an − 2 for n > 2
Find `(""^an +1)/(""^an")` for n = 1, 2, 3, 4, 5.
Which term of the A.P. 3, 8, 13, ... is 248?
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 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]
\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
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.
Find the sum of the following arithmetic progression :
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
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).
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.
Insert five numbers between 8 and 26 such that the resulting sequence is an 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.
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
If Sn denotes the sum of first n terms of an A.P. < an > such that
If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is
If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [cosec a1cosec a2 + cosec a1 cosec a3 + .... + cosec an − 1 cosec an] is
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
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 a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is ______.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
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 ______.
