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

Select the correct answer from the given alternative. If for a G.P. t6t3=145854 then r = ?

Advertisements
Advertisements

प्रश्न

Select the correct answer from the given alternative.

If for a G.P. `"t"_6/"t"_3 = 1458/54` then r = ?

पर्याय

  • 3

  • 2

  • 1

  • – 1

MCQ
Advertisements

उत्तर

3

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Sequences and Series - Miscellaneous Exercise 2.1 [पृष्ठ ४१]

APPEARS IN

बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
पाठ 2 Sequences and Series
Miscellaneous Exercise 2.1 | Q I. (3) | पृष्ठ ४१

संबंधित प्रश्‍न

Find the 20th and nthterms of the G.P. `5/2, 5/4 , 5/8,...`


How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?


Find the sum to n terms of the sequence, 8, 88, 888, 8888… .


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`.


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.


The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio `(3 + 2sqrt2) ":" (3 - 2sqrt2)`.


Show that one of the following progression is a G.P. Also, find the common ratio in case:

\[a, \frac{3 a^2}{4}, \frac{9 a^3}{16}, . . .\]


Which term of the progression 18, −12, 8, ... is \[\frac{512}{729}\] ?

 

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.


Evaluate the following:

\[\sum^{10}_{n = 2} 4^n\]


The 4th and 7th terms of a G.P. are \[\frac{1}{27} \text { and } \frac{1}{729}\] respectively. Find the sum of n terms of the G.P.


The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight 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.


Find the rational number whose decimal expansion is `0.4bar23`.


If a, b, c are in G.P., prove that log a, log b, log c are in A.P.


Find k such that k + 9, k − 6 and 4 form three consecutive terms of a G.P.


If a, b, c are in G.P., prove that:

\[a^2 b^2 c^2 \left( \frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{c^3} \right) = a^3 + b^3 + c^3\]


If a, b, c are in G.P., prove that:

\[\frac{1}{a^2 - b^2} + \frac{1}{b^2} = \frac{1}{b^2 - c^2}\]


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.:

a2 + b2, ab + bc, b2 + c2


If \[\frac{1}{a + b}, \frac{1}{2b}, \frac{1}{b + c}\] are three consecutive terms of an A.P., prove that a, b, c are the three consecutive terms of a G.P.


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


If the fifth term of a G.P. is 2, then write the product of its 9 terms.


If a, b, c are in G.P. and x, y are AM's between a, b and b,c respectively, then 


If x = (43) (46) (46) (49) .... (43x) = (0.0625)−54, the value of x is 


Mark the correct alternative in the following question: 

Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then p2R3 : S3 is equal to 


Check whether the following sequence is G.P. If so, write tn.

3, 4, 5, 6, …


Which term of the G.P. 5, 25, 125, 625, … is 510?


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


Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after 3 years.


For the following G.P.s, find Sn.

`sqrt(5)`, −5, `5sqrt(5)`, −25, ...


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


For a G.P. If t3 = 20 , t6 = 160 , find S7


Find: `sum_("r" = 1)^10 5 xx 3^"r"`


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×