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Select the correct answer from the given alternative. Which term of the geometric progression 1, 2, 4, 8, ... is 2048

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प्रश्न

Select the correct answer from the given alternative.

Which term of the geometric progression 1, 2, 4, 8, ... is 2048

पर्याय

  • 10th 

  • 11th 

  • 12th 

  • 13th 

MCQ
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उत्तर

12th 

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

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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. (4) | पृष्ठ ४१

संबंधित प्रश्‍न

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


The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7thterm.


If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P.


The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.


Find three numbers in G.P. whose sum is 65 and whose product is 3375.


The sum of first three terms of a G.P. is 13/12 and their product is − 1. Find the G.P.


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;


Evaluate the following:

\[\sum^n_{k = 1} ( 2^k + 3^{k - 1} )\]


Find the sum of the following series:

9 + 99 + 999 + ... to n terms;


Find the sum of the following serie to infinity:

`2/5 + 3/5^2 +2/5^3 + 3/5^4 + ... ∞.`


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.


The sum of first two terms of an infinite G.P. is 5 and each term is three times the sum of the succeeding terms. Find the G.P.


The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an A.P. Find the numbers.


If a, b, c are in G.P., prove that:

a (b2 + c2) = c (a2 + b2)


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

 (a + b + c + d)2 = (a + b)2 + 2 (b + c)2 + (c + d)2


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

(b + c) (b + d) = (c + a) (c + d)


If a, b, c are in G.P., prove that the following is also in G.P.:

a2, b2, c2


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

(a2 + b2 + c2), (ab + bc + cd), (b2 + c2 + d2) are in G.P.


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

\[\frac{a^2 + ab + b^2}{bc + ca + ab} = \frac{b + a}{c + b}\]

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 xa = xb/2 zb/2 = zc, then prove that \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.

  

Insert 5 geometric means between 16 and \[\frac{1}{4}\] .


If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is 


If S be the sum, P the product and R be the sum of the reciprocals of n terms of a GP, then P2 is equal to


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 


For a G.P. if S5 = 1023 , r = 4, Find a


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]


Express the following recurring decimal as a rational number:

`2.3bar(5)`


Select the correct answer from the given alternative.

If common ratio of the G.P is 5, 5th term is 1875, the first term is -


Select the correct answer from the given alternative.

Which of the following is not true, where A, G, H are the AM, GM, HM of a and b respectively. (a, b > 0)


Answer the following:

Find five numbers in G.P. such that their product is 243 and sum of second and fourth number is 10.


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


For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to ______.


Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.


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


Let A1, A2, A3, .... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = `1/1296` and A2 + A4 = `7/36`, then the value of A6 + A8 + A10 is equal to ______. 


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