Advertisements
Advertisements
प्रश्न
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Advertisements
उत्तर
Let the first term of the geometric progression = a
Common ratio = 2
12th term = a × 212−1 = 211 a
8th term = a × 28−1 = a × 27 = 128a
Given: 8th term = 192
∴ 128a = 192
or a = `192/128 = 3/2`
∴ 12th term = `1^11 xx 3/2`
= `2^10 xx 3`
= 1024 × 3
= 3072
APPEARS IN
संबंधित प्रश्न
Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.
If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that `a^(q - r) b^(r-p) c^(p-q) = 1`.
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P.
The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.
Find the sum of the following geometric series:
\[\frac{a}{1 + i} + \frac{a}{(1 + i )^2} + \frac{a}{(1 + i )^3} + . . . + \frac{a}{(1 + i )^n} .\]
Find the sum of the following series:
7 + 77 + 777 + ... to n terms;
Find the sum of the following series:
0.5 + 0.55 + 0.555 + ... to n terms.
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)th to (2n)th term is \[\frac{1}{r^n}\].
If a and b are the roots of x2 − 3x + p = 0 and c, d are the roots x2 − 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q − p) = 17 : 15.
Let an be the nth term of the G.P. of positive numbers.
Let \[\sum^{100}_{n = 1} a_{2n} = \alpha \text { and } \sum^{100}_{n = 1} a_{2n - 1} = \beta,\] such that α ≠ β. Prove that the common ratio of the G.P. is α/β.
Prove that: (21/4 . 41/8 . 81/16. 161/32 ... ∞) = 2.
Find the rational numbers having the following decimal expansion:
\[0 .\overline {231 }\]
If a, b, c, d are in G.P., prove that:
(a + b + c + d)2 = (a + b)2 + 2 (b + c)2 + (c + d)2
If a, b, c are in G.P., prove that the following is also in G.P.:
a2 + b2, ab + bc, b2 + c2
If a, b, c, d are in G.P., prove that:
(a2 + b2), (b2 + c2), (c2 + d2) are in G.P.
If a, b, c, d are in G.P., prove that:
\[\frac{1}{a^2 + b^2}, \frac{1}{b^2 - c^2}, \frac{1}{c^2 + d^2} \text { are in G . P } .\]
If a, b, c are in G.P., then prove that:
If pth, qth and rth terms of an A.P. and G.P. are both a, b and c respectively, show that \[a^{b - c} b^{c - a} c^{a - b} = 1\]
Insert 6 geometric means between 27 and \[\frac{1}{81}\] .
If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is \[\frac{9}{2}\], then write its first term and common difference.
If pth, qth and rth terms of a G.P. re x, y, z respectively, then write the value of xq − r yr − pzp − q.
If the first term of a G.P. a1, a2, a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is
If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is
In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is
The two geometric means between the numbers 1 and 64 are
Check whether the following sequence is G.P. If so, write tn.
2, 6, 18, 54, …
Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.
Find four numbers in G.P. such that sum of the middle two numbers is `10/3` and their product is 1
Find : `sum_("n" = 1)^oo 0.4^"n"`
A ball is dropped from a height of 10m. It bounces to a height of 6m, then 3.6m and so on. Find the total distance travelled by the ball
Select the correct answer from the given alternative.
If common ratio of the G.P is 5, 5th term is 1875, the first term is -
Answer the following:
If for a G.P. t3 = `1/3`, t6 = `1/81` find r
In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is ______.
The third term of G.P. is 4. The product of its first 5 terms is ______.
If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is ______.
If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
