मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

The numbers x − 6, 2x and x2 are in G.P. Find x

Advertisements
Advertisements

प्रश्न

The numbers x − 6, 2x and x2 are in G.P. Find x

बेरीज
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

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Sequences and Series - Exercise 2.1 [पृष्ठ २८]

APPEARS IN

संबंधित प्रश्‍न

The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.


For what values of x, the numbers  `-2/7, x, -7/2` are in G.P?


Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015,…


Find the sum to indicated number of terms of the geometric progressions `sqrt7, sqrt21,3sqrt7`...n terms.


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 `1/r^n`.


Find the value of n so that  `(a^(n+1) + b^(n+1))/(a^n + b^n)` may be the geometric mean between a and b.


Which term of the G.P. :

\[2, 2\sqrt{2}, 4, . . .\text {  is }128 ?\]


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 the sum of the following geometric progression:

1, −1/2, 1/4, −1/8, ... to 9 terms;


Find the sum of the following geometric series:

\[\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} + . . .\text { to 8  terms };\]


Find the sum of the following geometric series:

`sqrt7, sqrt21, 3sqrt7,...` 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 of the following series to infinity:

`1/3+1/5^2 +1/3^3+1/5^4 + 1/3^5 + 1/56+ ...infty`


Prove that: (21/4 . 41/8 . 81/16. 161/32 ... ∞) = 2.


Find the rational numbers having the following decimal expansion: 

\[0 .\overline {231 }\]


The sum of three numbers a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.


If a, b, c are in A.P. and a, b, d are in G.P., then prove that a, a − b, d − c are in G.P.


If pth, qth and rth terms of an A.P. and G.P. are both a, b and c respectively, show that \[a^{b - c} b^{c - a} c^{a - b} = 1\]


Find the geometric means of the following pairs of number:

2 and 8


If x is positive, the sum to infinity of the series \[\frac{1}{1 + x} - \frac{1 - x}{(1 + x )^2} + \frac{(1 - x )^2}{(1 + x )^3} - \frac{(1 - x )^3}{(1 + x )^4} + . . . . . . is\]


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.

`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...


For the G.P. if a = `2/3`, t6 = 162, find r.


The numbers 3, x, and x + 6 form are in G.P. Find nth term


For a G.P. if a = 2, r = 3, Sn = 242 find n


For a sequence, if Sn = 2(3n –1), find the nth term, hence show that the sequence is a G.P.


If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)5 = 1.47]


Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`1/2, 1/4, 1/8, 1/16,...`


Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`-3, 1, (-1)/3, 1/9, ...`


Express the following recurring decimal as a rational number:

`2.3bar(5)`


If the first term of the G.P. is 16 and its sum to infinity is `96/17` find the common ratio.


Find `sum_("r" = 0)^oo (-8)(-1/2)^"r"` 


The midpoints of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the areas of all the squares


A ball is dropped from a height of 10m. It bounces to a height of 6m, then 3.6m and so on. Find the total distance travelled by the ball


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.


If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.


If the pth and qth terms of a G.P. are q and p respectively, show that its (p + q)th term is `(q^p/p^q)^(1/(p - q))`


The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×