हिंदी

Select the correct answer from the given alternative. The common ratio for the G.P. 0.12, 0.24, 0.48, is – - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Select the correct answer from the given alternative.

The common ratio for the G.P. 0.12, 0.24, 0.48, is –

विकल्प

  • 0.12

  • 0.2

  • 0.02

  • 2

MCQ

उत्तर

The common ratio for the G.P. 0.12, 0.24, 0.48, is 2

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Sequences and Series - Miscellaneous Exercise 2.1 [पृष्ठ ४०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 2 Sequences and Series
Miscellaneous Exercise 2.1 | Q I. (1) | पृष्ठ ४०

संबंधित प्रश्न

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`.


Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn


If a and b are the roots of are roots of x2 – 3x + p = 0 , and c, d are roots of x2 – 12x + q = 0, where a, b, c, d, form a G.P. Prove that (q + p): (q – p) = 17 : 15.


Which term of the G.P. :

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


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

 

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 progression:

1, −1/2, 1/4, −1/8, ... to 9 terms;


Find the sum of the following geometric progression:

(a2 − b2), (a − b), \[\left( \frac{a - b}{a + b} \right)\] to n terms;


Find the sum of the following geometric series:

 0.15 + 0.015 + 0.0015 + ... to 8 terms;


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.


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.


If a, b, c, d are in G.P., prove that:

(b + c) (b + d) = (c + a) (c + d)


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.


Insert 5 geometric means between \[\frac{32}{9}\text{and}\frac{81}{2}\] .


Find the geometric means of the following pairs of number:

a3b and ab3


If logxa, ax/2 and logb x are in G.P., then write the value of x.


If the first term of a G.P. a1a2a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is


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.

1, –5, 25, –125 …


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

7, 14, 21, 28, …


For the G.P. if a = `7/243`, r = 3 find t6.


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.


Find the sum to n terms of the sequence.

0.5, 0.05, 0.005, ...


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


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:

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


Find GM of two positive numbers whose A.M. and H.M. are 75 and 48


If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by `18/5`, find the numbers.


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:

Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.


Answer the following:

If p, q, r, s are in G.P., show that (p2 + q2 + r2) (q2 + r2 + s2) = (pq + qr + rs)2   


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 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 ______.


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 ______.


If 0 < x, y, a, b < 1, then the sum of the infinite terms of the series `sqrt(x)(sqrt(a) + sqrt(x)) + sqrt(x)(sqrt(ab) + sqrt(xy)) + sqrt(x)(bsqrt(a) + ysqrt(x)) + ...` is ______.


If the expansion in powers of x of the function `1/((1 - ax)(1 - bx))` is a0 + a1x + a2x2 + a3x3 ....... then an is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.