मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Check whether the following sequence is G.P. If so, write tn. 7, 14, 21, 28, … - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

7, 14, 21, 28, …

बेरीज

उत्तर

7, 14, 21, 28, …

t1 = 7, t2 = 14, t3 = 21, t4 = 28

Here, `"t"_2/"t"_1` = 2, `"t"_3/"t"_2 = 3/2`, `"t"_4/"t"_3 = 4/3`

∵ `"t"_2/"t"_1 ≠ "t"_3/"t"_2 ≠ "t"_4/"t"_3`

∴ the sequence is not a Geometric progression.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Sequences and Series - Exercise 2.1 [पृष्ठ २७]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 2 Sequences and Series
Exercise 2.1 | Q 1. (v) | पृष्ठ २७

संबंधित प्रश्‍न

Which term of the following sequence:

`1/3, 1/9, 1/27`, ...., is `1/19683`?


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


If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.


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 `1/r^n`.


Insert two numbers between 3 and 81 so that the resulting sequence is 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:

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


Show that the sequence <an>, defined by an = \[\frac{2}{3^n}\], n ϵ N is a G.P.


Which term of the G.P. :

\[\sqrt{3}, 3, 3\sqrt{3}, . . . \text { is } 729 ?\]


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

 

In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.


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 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers are in A.P. Find the numbers.


Find the sum of the following geometric series:

\[\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} + . . .\text { to 8  terms };\]


Find the sum of the following geometric series:

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


Find the sum of the following series:

0.5 + 0.55 + 0.555 + ... to n terms.


Find the sum :

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


If a and b are the roots of x2 − 3x + p = 0 and c, d are the roots x2 − 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q − p) = 17 : 15.


Find the sum of the terms of an infinite decreasing G.P. in which all the terms are positive, the first term is 4, and the difference between the third and fifth term is equal to 32/81.


Show that in an infinite G.P. with common ratio r (|r| < 1), each term bears a constant ratio to the sum of all terms that follow it.


If S denotes the sum of an infinite G.P. S1 denotes the sum of the squares of its terms, then prove that the first term and common ratio are respectively

\[\frac{2S S_1}{S^2 + S_1}\text {  and } \frac{S^2 - S_1}{S^2 + S_1}\]


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 the following is also in G.P.:

a2, b2, c2


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

a3, b3, c3


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


Find the geometric means of the following pairs of number:

−8 and −2


The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio \[(3 + 2\sqrt{2}) : (3 - 2\sqrt{2})\] .


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 


The two geometric means between the numbers 1 and 64 are 


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

2, 6, 18, 54, …


Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.


The number of bacteria in a culture doubles every hour. If there were 50 bacteria originally in the culture, how many bacteria will be there at the end of 5thhour?


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


Find : `sum_("r" = 1)^oo 4(0.5)^"r"`


Select the correct answer from the given alternative.

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


Answer the following:

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


If the pth and qth terms of a G.P. are q and p respectively, show that its (p + q)th term is `(q^p/p^q)^(1/(p - q))`


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×