Advertisements
Advertisements
प्रश्न
Find the geometric means of the following pairs of number:
a3b and ab3
Advertisements
उत्तर
\[\text { Let the G . M . between }a^3 \text { b and a } b^3 \text { be G } . \]
\[\text { Then,} a^3 \text { b, G and } a b^3 \text { are in G . P } . \]
\[ \therefore G^2 = a^3 b \times a b^3 \]
\[ \Rightarrow G^2 = a^4 b^4 \]
\[ \Rightarrow G = \sqrt{a^4 b^4}\]
\[ \Rightarrow G = a^2 b^2\]
संबंधित प्रश्न
Evaluate `sum_(k=1)^11 (2+3^k )`
Which term of the G.P. :
\[\frac{1}{3}, \frac{1}{9}, \frac{1}{27} . . \text { . is } \frac{1}{19683} ?\]
The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.
In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.
Find three numbers in G.P. whose sum is 38 and their product is 1728.
Find the sum of the following geometric series:
`sqrt7, sqrt21, 3sqrt7,...` to n terms
Evaluate the following:
\[\sum^{11}_{n = 1} (2 + 3^n )\]
Evaluate the following:
\[\sum^n_{k = 1} ( 2^k + 3^{k - 1} )\]
Evaluate the following:
\[\sum^{10}_{n = 2} 4^n\]
Find the sum of the following serie:
5 + 55 + 555 + ... to n terms;
Find the sum of the following series:
0.6 + 0.66 + 0.666 + .... to n terms
How many terms of the G.P. 3, 3/2, 3/4, ... be taken together to make \[\frac{3069}{512}\] ?
Find the sum :
\[\sum^{10}_{n = 1} \left[ \left( \frac{1}{2} \right)^{n - 1} + \left( \frac{1}{5} \right)^{n + 1} \right] .\]
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.
Find the sum of the following serie to infinity:
`2/5 + 3/5^2 +2/5^3 + 3/5^4 + ... ∞.`
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 pth, qth, rth and sth terms of an A.P. be in G.P., then prove that p − q, q − r, r − s 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.
Insert 5 geometric means between \[\frac{32}{9}\text{and}\frac{81}{2}\] .
If logxa, ax/2 and logb x are in G.P., then write the value of x.
The fractional value of 2.357 is
If x = (43) (46) (46) (49) .... (43x) = (0.0625)−54, the value of x is
Let x be the A.M. and y, z be two G.M.s between two positive numbers. Then, \[\frac{y^3 + z^3}{xyz}\] is equal to
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
The numbers x − 6, 2x and x2 are in G.P. Find x
For a G.P. sum of first 3 terms is 125 and sum of next 3 terms is 27, find the value of r
For a G.P. If t3 = 20 , t6 = 160 , find S7
For a G.P. If t4 = 16, t9 = 512, find S10
Express the following recurring decimal as a rational number:
`2.bar(4)`
If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by `18/5`, find the numbers.
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
Answer the following:
If pth, qth and rth terms of a G.P. are x, y, z respectively. Find the value of xq–r .yr–p .zp–q
Answer the following:
If p, q, r, s are in G.P., show that (pn + qn), (qn + rn) , (rn + sn) are also in G.P.
For an increasing G.P. a1, a2 , a3 ........., an, if a6 = 4a4, a9 – a7 = 192, then the value of `sum_(i = 1)^∞ 1/a_i` is ______.
