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
Which term of the following sequence:
`sqrt3, 3, 3sqrt3`, .... is 729?
Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.
Which term of the progression 18, −12, 8, ... is \[\frac{512}{729}\] ?
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.
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 series:
\[\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . \text { to 5 terms };\]
How many terms of the G.P. 3, 3/2, 3/4, ... be taken together to make \[\frac{3069}{512}\] ?
Find the sum of the following serie to infinity:
8 + \[4\sqrt{2}\] + 4 + ... ∞
Find the rational numbers having the following decimal expansion:
\[3 . 5\overline 2\]
If a, b, c are in G.P., prove that the following is also in G.P.:
a2, b2, c2
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 (a − b), (b − c), (c − a) are in G.P., then prove that (a + b + c)2 = 3 (ab + bc + ca)
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., b,c,d are in G.P. and \[\frac{1}{c}, \frac{1}{d}, \frac{1}{e}\] are in A.P., prove that a, c,e are in G.P.
If (p + q)th and (p − q)th terms of a G.P. are m and n respectively, then write is pth term.
If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms, then its first term is
If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is
If p, q be two A.M.'s and G be one G.M. between two numbers, then G2 =
Check whether the following sequence is G.P. If so, write tn.
7, 14, 21, 28, …
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
For the following G.P.s, find Sn
0.7, 0.07, 0.007, .....
For a G.P. if S5 = 1023 , r = 4, Find a
For a G.P. if a = 2, r = 3, Sn = 242 find n
The value of a house appreciates 5% per year. How much is the house worth after 6 years if its current worth is ₹ 15 Lac. [Given: (1.05)5 = 1.28, (1.05)6 = 1.34]
Find : `sum_("r" = 1)^oo 4(0.5)^"r"`
Select the correct answer from the given alternative.
The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is –
Answer the following:
If a, b, c are in G.P. and ax2 + 2bx + c = 0 and px2 + 2qx + r = 0 have common roots then verify that pb2 – 2qba + ra2 = 0
Answer the following:
Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`
If a, b, c, d are four distinct positive quantities in G.P., then show that a + d > b + c
In a G.P. of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P. is ______.
The third term of G.P. is 4. The product of its first 5 terms 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 ______.
If `e^((cos^2x + cos^4x + cos^6x + ...∞)log_e2` satisfies the equation t2 – 9t + 8 = 0, then the value of `(2sinx)/(sinx + sqrt(3)cosx)(0 < x ,< π/2)` is ______.
If the expansion in powers of x of the function `1/((1 - ax)(1 - bx))` is a0 + a1x + a2x2 + a3x3 ....... then an is ______.
