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 the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Given a G.P. with a = 729 and 7th term 64, determine S7.
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.
The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio `(3 + 2sqrt2) ":" (3 - 2sqrt2)`.
Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn
Find :
the 12th term of the G.P.
\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]
If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.
Find the sum of the following geometric progression:
2, 6, 18, ... to 7 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:
\[\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . \text { to 5 terms };\]
Evaluate the following:
\[\sum^{11}_{n = 1} (2 + 3^n )\]
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 series:
0.5 + 0.55 + 0.555 + ... to n terms.
How many terms of the G.P. 3, 3/2, 3/4, ... be taken together to make \[\frac{3069}{512}\] ?
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 \[\frac{1}{r^n}\].
Find the rational number whose decimal expansion is `0.4bar23`.
If a, b, c are in G.P., prove that the following is also in G.P.:
a2 + b2, ab + bc, b2 + c2
If \[\frac{1}{a + b}, \frac{1}{2b}, \frac{1}{b + c}\] are three consecutive terms of an A.P., prove that a, b, c are the three consecutive terms of a G.P.
Find the geometric means of the following pairs of number:
−8 and −2
If the fifth term of a G.P. is 2, then write the product of its 9 terms.
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
The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then its first term is ______.
If A be one A.M. and p, q be two G.M.'s between two numbers, then 2 A is equal to
The numbers 3, x, and x + 6 form are in G.P. Find 20th term.
For the following G.P.s, find Sn
0.7, 0.07, 0.007, .....
For the following G.P.s, find Sn.
`sqrt(5)`, −5, `5sqrt(5)`, −25, ...
For a G.P. sum of first 3 terms is 125 and sum of next 3 terms is 27, find the value of r
Find the sum to n terms of the sequence.
0.2, 0.02, 0.002, ...
Express the following recurring decimal as a rational number:
`0.bar(7)`
If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term
Answer the following:
Find the sum of the first 5 terms of the G.P. whose first term is 1 and common ratio is `2/3`
Answer the following:
If for a G.P. t3 = `1/3`, t6 = `1/81` find r
At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was Rs 1250, find the value at the end of 5 years.
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 third term of a G.P. is 4, the product of the first five terms is ______.
Let A1, A2, A3, .... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = `1/1296` and A2 + A4 = `7/36`, then the value of A6 + A8 + A10 is equal to ______.
