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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

MCQ

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

संबंधित प्रश्‍न

The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.


Insert two numbers between 3 and 81 so that the resulting sequence is G.P.


Find the value of n so that  `(a^(n+1) + b^(n+1))/(a^n + b^n)` may be the geometric mean between a and b.


if `(a+ bx)/(a - bx) = (b +cx)/(b - cx) = (c + dx)/(c- dx) (x != 0)` then show that a, b, c and d are in G.P.


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

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


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

\[\frac{2}{27}, \frac{2}{9}, \frac{2}{3}, . . . , 162\]

Find the sum of the following geometric progression:

1, 3, 9, 27, ... to 8 terms;


Find the sum of the following geometric series:

1, −a, a2, −a3, ....to n terms (a ≠ 1)


Find the sum of the following geometric series:

x3, x5, x7, ... to n terms


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:

0.5 + 0.55 + 0.555 + ... to n terms.


Find the sum of the following series:

0.6 + 0.66 + 0.666 + .... to n 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.


The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.


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 \[\frac{1}{r^n}\].


Find the rational numbers having the following decimal expansion: 

\[0 . 6\overline8\]


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

a3, b3, c3


If (a − b), (b − c), (c − a) are in G.P., then prove that (a + b + c)2 = 3 (ab + bc + ca)


If a, b, c are three distinct real numbers in G.P. and a + b + c = xb, then prove that either x< −1 or x > 3.


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


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

 


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

7, 14, 21, 28, …


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


For the G.P. if r = − 3 and t6 = 1701, find a.


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


Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.


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


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 n years.


Select the correct answer from the given alternative.

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


Answer the following:

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


Answer the following:

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


Answer the following:

For a G.P. if t2 = 7, t4 = 1575 find a


Answer the following:

If for a G.P. t3 = `1/3`, t6 = `1/81` find r


Answer the following:

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


Answer the following:

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


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


If `e^((cos^2x + cos^4x + cos^6x + ...∞)log_e2` satisfies the equation t2 – 9t + 8 = 0, then the value of `(2sinx)/(sinx + sqrt(3)cosx)(0 < x ,< π/2)` is ______.


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


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