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Select the correct answer from the given alternative. The sum of 3 terms of a G.P. is 214 and their product is 1 then the common ratio is – - Mathematics and Statistics

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प्रश्न

Select the correct answer from the given alternative.

The sum of 3 terms of a G.P. is `21/4` and their product is 1 then the common ratio is –

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उत्तर

The sum of 3 terms of a G.P. is `21/4` and their product is 1 then the common ratio is 4

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पाठ 2: Sequences and Series - Miscellaneous Exercise 2.1 [पृष्ठ ४१]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 2 Sequences and Series
Miscellaneous Exercise 2.1 | Q I. (6) | पृष्ठ ४१

संबंधित प्रश्‍न

Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).


Evaluate `sum_(k=1)^11 (2+3^k )`


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`


A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.


Find:

the 10th term of the G.P.

\[- \frac{3}{4}, \frac{1}{2}, - \frac{1}{3}, \frac{2}{9}, . . .\]

 


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

 

Find the 4th term from the end of the G.P.

\[\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, . . . , \frac{1}{4374}\]


If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.


If \[\frac{a + bx}{a - bx} = \frac{b + cx}{b - cx} = \frac{c + dx}{c - dx}\] (x ≠ 0), then show that abc and d are in G.P.


Find the sum of the following geometric series:

\[\frac{a}{1 + i} + \frac{a}{(1 + i )^2} + \frac{a}{(1 + i )^3} + . . . + \frac{a}{(1 + i )^n} .\]


Find the sum of the following geometric series:

\[\sqrt{7}, \sqrt{21}, 3\sqrt{7}, . . .\text {  to n terms }\]


Find the sum of the following series:

7 + 77 + 777 + ... to n terms;


Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.


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

  

Insert 6 geometric means between 27 and  \[\frac{1}{81}\] .


If (p + q)th and (p − q)th terms of a G.P. are m and n respectively, then write is pth term.


If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is \[\frac{9}{2}\], then write its first term and common difference.


The fractional value of 2.357 is 


If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is


If pq be two A.M.'s and G be one G.M. between two numbers, then G2


In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is 


The fifth term of a G.P. is x, eighth term of a G.P. is y and eleventh term of a G.P. is z verify whether y2 = xz


If p, q, r, s are in G.P. show that p + q, q + r, r + s are also in G.P.


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?


For a G.P. a = 2, r = `-2/3`, find S6


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


If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term


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 perimeters of all the squares


Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.


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.

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:

For a sequence , if tn = `(5^("n" - 2))/(7^("n" - 3))`, verify whether the sequence is a G.P. If it is a G.P., find its first term and the common ratio.


Answer the following:

Find k so that k – 1, k, k + 2 are consecutive terms of a G.P.


Answer the following:

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


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 ______.


The third term of a G.P. is 4, the product of the first five terms is ______.


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