Advertisements
Advertisements
प्रश्न
The numbers 3, x, and x + 6 form are in G.P. Find x
Advertisements
उत्तर
The numbers 3, x, and x + 6 are in G.P.
∴ `"x"/3 = ("x" + 6)/"x"`
∴ x2 = 3x + 18
∴ x2 – 3x – 18 = 0
∴ (x – 6)(x + 3) = 0
∴ x – 6 = 0 or x + 3 = 0
∴ x = 6 or x = – 3
APPEARS IN
संबंधित प्रश्न
The sum of first three terms of a G.P. is `39/10` and their product is 1. Find the common ratio and the terms.
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`.
If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.
Find:
the 10th term of the G.P.
\[- \frac{3}{4}, \frac{1}{2}, - \frac{1}{3}, \frac{2}{9}, . . .\]
Which term of the G.P. :
\[\frac{1}{3}, \frac{1}{9}, \frac{1}{27} . . \text { . is } \frac{1}{19683} ?\]
Find three numbers in G.P. whose sum is 65 and whose product is 3375.
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 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:
(x +y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3) + ... to n terms;
Find the sum of the following geometric series:
x3, x5, x7, ... to n terms
How many terms of the series 2 + 6 + 18 + ... must be taken to make the sum equal to 728?
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: (91/3 . 91/9 . 91/27 ... ∞) = 3.
Find the rational numbers having the following decimal expansion:
\[0 .\overline {231 }\]
If a, b, c are in G.P., prove that \[\frac{1}{\log_a m}, \frac{1}{\log_b m}, \frac{1}{\log_c m}\] are in A.P.
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 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 second term of a G.P. is 2 and the sum of its infinite terms is 8, 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
Given that x > 0, the sum \[\sum^\infty_{n = 1} \left( \frac{x}{x + 1} \right)^{n - 1}\] equals
Check whether the following sequence is G.P. If so, write tn.
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...
If for a sequence, tn = `(5^("n"-3))/(2^("n"-3))`, show that the sequence is a G.P. Find its first term and the common ratio
Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.
Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.
The numbers 3, x, and x + 6 form are in G.P. Find 20th term.
For the following G.P.s, find Sn.
p, q, `"q"^2/"p", "q"^3/"p"^2,` ...
Select the correct answer from the given alternative.
The common ratio for the G.P. 0.12, 0.24, 0.48, is –
Select the correct answer from the given alternative.
If for a G.P. `"t"_6/"t"_3 = 1458/54` then r = ?
The sum of 3 terms of a G.P. is `21/4` and their product is 1 then the common ratio is ______.
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:
For a G.P. a = `4/3` and t7 = `243/1024`, find the value of r
Answer the following:
If for a G.P. first term is (27)2 and seventh term is (8)2, find S8
Answer the following:
Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.
Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.
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 ______.
The sum of infinite number of terms of a decreasing G.P. is 4 and the sum of the terms to m squares of its terms to infinity is `16/3`, then the G.P. is ______.
