Advertisements
Advertisements
Question
Find GM of two positive numbers whose A.M. and H.M. are 75 and 48
Advertisements
Solution
A.M. = 75, H.M. = 48
∵ (G.M.)2 = (A.M.) (H.M.)
∴ (G.M.)2 = 75 × 48
= 25 × 3 × 16 × 3
= 52 × 42 × 32
∴ G.M. = 5 × 4 × 3
∴ G.M. = 60
APPEARS IN
RELATED QUESTIONS
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 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
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.
Which term of the progression 18, −12, 8, ... is \[\frac{512}{729}\] ?
Find the 4th term from the end of the G.P.
\[\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, . . . , \frac{1}{4374}\]
Find three numbers in G.P. whose sum is 38 and their product is 1728.
The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.
Find the sum of the following geometric progression:
1, 3, 9, 27, ... to 8 terms;
Find the sum of the following geometric series:
\[\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . \text { to 5 terms };\]
Find the sum of the following geometric series:
`sqrt7, sqrt21, 3sqrt7,...` to n terms
Find the sum of the following serie:
5 + 55 + 555 + ... to n terms;
Find the sum of the following series:
9 + 99 + 999 + ... to n terms;
Find the sum of the following serie to infinity:
\[1 - \frac{1}{3} + \frac{1}{3^2} - \frac{1}{3^3} + \frac{1}{3^4} + . . . \infty\]
Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.
Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.
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, d are in G.P., prove that:
(a2 + b2), (b2 + c2), (c2 + d2) are in G.P.
If a, b, c are in A.P. and a, b, d are in G.P., show that a, (a − b), (d − c) 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 5 geometric means between 16 and \[\frac{1}{4}\] .
The value of 91/3 . 91/9 . 91/27 ... upto inf, is
If x = (43) (46) (46) (49) .... (43x) = (0.0625)−54, the value of x is
The product (32), (32)1/6 (32)1/36 ... to ∞ is equal to
Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.
The fifth term of a G.P. is x, eighth term of a G.P. is y and eleventh term of a G.P. is z verify whether y2 = xz
A ball is dropped from a height of 80 ft. The ball is such that it rebounds `(3/4)^"th"` of the height it has fallen. How high does the ball rebound on 6th bounce? How high does the ball rebound on nth bounce?
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.
For a G.P. a = 2, r = `-2/3`, find S6
Find the sum to n terms of the sequence.
0.2, 0.02, 0.002, ...
Express the following recurring decimal as a rational number:
`2.3bar(5)`
Find : `sum_("r" = 1)^oo 4(0.5)^"r"`
Answer the following:
In a G.P., the fourth term is 48 and the eighth term is 768. Find the tenth term
Answer the following:
Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...
Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then P2 R3 : S3 is equal to ______.
The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in ______.
