Advertisements
Advertisements
प्रश्न
The numbers x − 6, 2x and x2 are in G.P. Find x
Advertisements
उत्तर
The numbers x − 6, 2x and x2 are in G.P.
∴ `(2x)/(x - 6) = x^2/(2x)`
∴ 4x2 = x2(x – 6)
∴ 4 = x – 6 ...[∵ x2 ≠ 0]
∴ x = 10
APPEARS IN
संबंधित प्रश्न
Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
Show that one of the following progression is a G.P. Also, find the common ratio in case:
4, −2, 1, −1/2, ...
Show that the sequence <an>, defined by an = \[\frac{2}{3^n}\], n ϵ N is a G.P.
Find :
the 12th term of the G.P.
\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]
Find :
nth term of the G.P.
\[\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3\sqrt{3}}, . . .\]
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.
Find the sum of the following geometric series:
`3/5 + 4/5^2 + 3/5^3 + 4/5^4 + ....` to 2n terms;
Find the sum of the following geometric series:
\[\frac{a}{1 + i} + \frac{a}{(1 + i )^2} + \frac{a}{(1 + i )^3} + . . . + \frac{a}{(1 + i )^n} .\]
Find the sum of the following geometric series:
`sqrt7, sqrt21, 3sqrt7,...` to n terms
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.
If S1, S2, ..., Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ..., n respectively, then prove that S1 + S2 + 2S3 + 3S4 + ... (n − 1) Sn = 1n + 2n + 3n + ... + nn.
Find the sum of 2n terms of the series whose every even term is 'a' times the term before it and every odd term is 'c' times the term before it, the first term being unity.
Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.
Prove that: (21/4 . 41/8 . 81/16. 161/32 ... ∞) = 2.
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.:
a3, b3, c3
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.
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 ______.
Check whether the following sequence is G.P. If so, write tn.
2, 6, 18, 54, …
Check whether the following sequence is G.P. If so, write tn.
1, –5, 25, –125 …
The numbers 3, x, and x + 6 form are in G.P. Find 20th term.
For the following G.P.s, find Sn
3, 6, 12, 24, ...
For the following G.P.s, find Sn.
`sqrt(5)`, −5, `5sqrt(5)`, −25, ...
For a G.P. if S5 = 1023 , r = 4, Find a
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.
0.5, 0.05, 0.005, ...
Find: `sum_("r" = 1)^10 5 xx 3^"r"`
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
9, 8.1, 7.29, ...
Express the following recurring decimal as a rational number:
`0.bar(7)`
Express the following recurring decimal as a rational number:
`2.bar(4)`
Express the following recurring decimal as a rational number:
`2.3bar(5)`
Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.
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 three numbers in G.P. such that their sum is 35 and their product is 1000
Answer the following:
Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...
Answer the following:
Find `sum_("r" = 1)^"n" (2/3)^"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.
If the sum of an infinite GP a, ar, ar2, ar3, ...... . is 15 and the sum of the squares of its each term is 150, then the sum of ar2, ar4, ar6, .... is ______.
