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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 - - Mathematics and Statistics

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प्रश्न

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 -

पर्याय

  • 3

  • 5

  • 15

  • – 5

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उत्तर

If common ratio of the G.P is 5, 5th term is 1875, the first term is 3

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  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 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 2 Sequences and Series
Miscellaneous Exercise 2.1 | Q I. (5) | पृष्ठ ४१

संबंधित प्रश्‍न

Which term of the following sequence: 

`2, 2sqrt2, 4,.... is 128`


For what values of x, the numbers  `-2/7, x, -7/2` are in G.P?


Find the sum to indicated number of terms in the geometric progressions x3, x5, x7, ... n terms (if x ≠ ± 1).


Given a G.P. with a = 729 and 7th term 64, determine S7.


If a, b, c and d are in G.P. show that (a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2 .


The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.


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

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


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


The 4th term of a G.P. is square of its second term, and the first term is − 3. Find its 7th term.


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:

(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;


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`


If Sp denotes the sum of the series 1 + rp + r2p + ... to ∞ and sp the sum of the series 1 − rp + r2p − ... to ∞, prove that Sp + sp = 2 . S2p.


Three numbers are in A.P. and their sum is 15. If 1, 3, 9 be added to them respectively, they form a G.P. Find the numbers.


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

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


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

  

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


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

 


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


If x is positive, the sum to infinity of the series \[\frac{1}{1 + x} - \frac{1 - x}{(1 + x )^2} + \frac{(1 - x )^2}{(1 + x )^3} - \frac{(1 - x )^3}{(1 + x )^4} + . . . . . . is\]


For the G.P. if r = `1/3`, a = 9 find t7


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


The numbers x − 6, 2x and x2 are in G.P. Find 1st term


For the following G.P.s, find Sn

3, 6, 12, 24, ...


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

p, q, `"q"^2/"p", "q"^3/"p"^2,` ...


For the following G.P.s, find Sn

0.7, 0.07, 0.007, .....


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


If S, P, R are the sum, product, and sum of the reciprocals of n terms of a G.P. respectively, then verify that `["S"/"R"]^"n"` = P


Find: `sum_("r" = 1)^10(3 xx 2^"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]


Express the following recurring decimal as a rational number:

`2.3bar(5)`


Express the following recurring decimal as a rational number:

`51.0bar(2)`


Select the correct answer from the given alternative.

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


Answer the following:

Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...


Answer the following:

Find `sum_("r" = 1)^"n" (2/3)^"r"`


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 ______.


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