Advertisements
Advertisements
Question
Select the correct answer from the given alternative.
The common ratio for the G.P. 0.12, 0.24, 0.48, is –
Options
0.12
0.2
0.02
2
Advertisements
Solution
The common ratio for the G.P. 0.12, 0.24, 0.48, is 2
APPEARS IN
RELATED QUESTIONS
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7thterm.
Find the sum to indicated number of terms of the geometric progressions `sqrt7, sqrt21,3sqrt7`...n terms.
Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.
Find the sum of the products of the corresponding terms of the sequences `2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2`
Show that the products of the corresponding terms of the sequences a, ar, ar2, …arn – 1 and A, AR, AR2, … `AR^(n-1)` form a G.P, and find the common ratio
If f is a function satisfying f (x +y) = f(x) f(y) for all x, y ∈ N such that f(1) = 3 and `sum_(x = 1)^n` f(x) = 120, find the value of n.
Show that one of the following progression is a G.P. Also, find the common ratio in case:
−2/3, −6, −54, ...
Find :
the 8th term of the G.P. 0.3, 0.06, 0.012, ...
Find :
the 12th term of the G.P.
\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]
Find the 4th term from the end of the G.P.
\[\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, . . . , \frac{1}{4374}\]
The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.
If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.
If 5th, 8th and 11th terms of a G.P. are p. q and s respectively, prove that q2 = ps.
The sum of first three terms of a G.P. is \[\frac{39}{10}\] and their product is 1. Find the common ratio and the terms.
Find the sum of the following geometric progression:
1, 3, 9, 27, ... to 8 terms;
Find the sum of the following geometric progression:
(a2 − b2), (a − b), \[\left( \frac{a - b}{a + b} \right)\] to n terms;
Find the sum of the following geometric series:
\[\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} + . . .\text { to 8 terms };\]
Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.
Show that in an infinite G.P. with common ratio r (|r| < 1), each term bears a constant ratio to the sum of all terms that follow it.
If a, b, c are in G.P., prove that log a, log b, log c are in A.P.
The sum of three numbers which are consecutive terms of an A.P. is 21. If the second number is reduced by 1 and the third is increased by 1, we obtain three consecutive terms of a G.P. Find the numbers.
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.:
a3, b3, c3
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:
(a2 − b2), (b2 − c2), (c2 − d2) are in G.P.
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 A1, A2 be two AM's and G1, G2 be two GM's between a and b, then find the value of \[\frac{A_1 + A_2}{G_1 G_2}\]
If x = (43) (46) (46) (49) .... (43x) = (0.0625)−54, the value of x is
The two geometric means between the numbers 1 and 64 are
Check whether the following sequence is G.P. If so, write tn.
7, 14, 21, 28, …
Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.
Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after 10 years.
Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after n years.
The numbers x − 6, 2x and x2 are in G.P. Find 1st term
Find : `sum_("r" = 1)^oo (-1/3)^"r"`
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
Answer the following:
For a sequence Sn = 4(7n – 1) verify that the sequence is a G.P.
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 ______.
The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252cm2. The length of the longest edge is ______.
