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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct answer from the given alternative. The tenth term of the geometric sequence 14,-12,1,-2, ... is –

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प्रश्न

Select the correct answer from the given alternative.

The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is –

पर्याय

  • 1024

  • `1/1024`

  • – 128

  • `(-1)/28`

MCQ
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उत्तर

The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is – 128

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पाठ 2: Sequences and Series - Miscellaneous Exercise 2.1 [पृष्ठ ४०]

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

संबंधित प्रश्‍न

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


The sum of first three terms of a G.P. is  `39/10` and their product is 1. Find the common ratio and the terms.


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


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

−2/3, −6, −54, ...


Find :

the 10th term of the G.P.

\[\sqrt{2}, \frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}, . . .\]


Which term of the G.P.: `sqrt3, 3, 3sqrt3`, ... is 729?


If a, b, c, d and p are different real numbers such that:
(a2 + b2 + c2) p2 − 2 (ab + bc + cd) p + (b2 + c2 + d2) ≤ 0, then show that a, b, c and d are in G.P.


The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.


Find the sum :

\[\sum^{10}_{n = 1} \left[ \left( \frac{1}{2} \right)^{n - 1} + \left( \frac{1}{5} \right)^{n + 1} \right] .\]


How many terms of the G.P. `3, 3/2, 3/4` ..... are needed to give the sum `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`


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 + 2b + 2c) (a − 2b + 2c) = a2 + 4c2.


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

  

If a, b, c are in A.P. and a, b, d are in G.P., show that a, (a − b), (d − c) are in G.P.


Write the product of n geometric means between two numbers a and b

 


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


The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 92. The common ratio of the original G.P. is 


If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms, then its first term 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.

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


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

7, 14, 21, 28, …


If for a sequence, tn = `(5^("n"-3))/(2^("n"-3))`, show that the sequence is a G.P. Find its first term and the common ratio


Find four numbers in G.P. such that sum of the middle two numbers is `10/3` and their product is 1


A ball is dropped from a height of 80 ft. The ball is such that it rebounds `(3/4)^"th"` of the height it has fallen. How high does the ball rebound on 6th bounce? How high does the ball rebound on nth bounce?


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


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


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:

Find three numbers in G.P. such that their sum is 35 and their product is 1000


Answer the following:

If for a G.P. first term is (27)2 and seventh term is (8)2, find S8 


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:

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


Answer the following:

Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`


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 ______.


If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is ______.


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 ______.


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