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

For the following G.P.s, find Sn 3, 6, 12, 24, ... - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

For the following G.P.s, find Sn

3, 6, 12, 24, ...

बेरीज
Advertisements

उत्तर

3, 6, 12, 24, …

Here, a = 3, r = `6/3` = 2 > 1

Sn = `("a"("r"^"n" - 1))/("r" - 1)`, for r > 1

∴ Sn = `(3(2^"n" - 1))/(2 - 1)`

Sn = 3(2n – 1)

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Sequences and Series - Exercise 2.2 [पृष्ठ ३१]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 2 Sequences and Series
Exercise 2.2 | Q 1. (i) | पृष्ठ ३१

संबंधित प्रश्‍न

Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015,…


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


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


The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.


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.


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, ...


Which term of the G.P. :

\[\frac{1}{3}, \frac{1}{9}, \frac{1}{27} . . \text { . is } \frac{1}{19683} ?\]


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

 

The sum of first three terms of a G.P. is 13/12 and their product is − 1. Find the G.P.


Find three numbers in G.P. whose product is 729 and the sum of their products in pairs is 819.


If S1, S2, S3 be respectively the sums of n, 2n, 3n terms of a G.P., then prove that \[S_1^2 + S_2^2\] = S1 (S2 + S3).


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


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

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


If a, b, c are in G.P., prove that:

a (b2 + c2) = c (a2 + b2)


If a, b, c are in G.P., prove that:

\[a^2 b^2 c^2 \left( \frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{c^3} \right) = a^3 + b^3 + c^3\]


If a, b, c are in G.P., prove that:

\[\frac{(a + b + c )^2}{a^2 + b^2 + c^2} = \frac{a + b + c}{a - b + c}\]


If a, b, c are in G.P., prove that:

\[\frac{1}{a^2 - b^2} + \frac{1}{b^2} = \frac{1}{b^2 - c^2}\]


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


If logxa, ax/2 and logb x are in G.P., then write the value of x.


If the first term of a G.P. a1a2a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is


If pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is


The value of 91/3 . 91/9 . 91/27 ... upto inf, 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 x is positive, the sum to infinity of the series \[\frac{1}{1 + x} - \frac{1 - x}{(1 + x )^2} + \frac{(1 - x )^2}{(1 + x )^3} - \frac{(1 - x )^3}{(1 + x )^4} + . . . . . . is\]


The two geometric means between the numbers 1 and 64 are 


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


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 5th hour?


The numbers 3, x, and x + 6 form are in G.P. Find 20th term.


Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

9, 8.1, 7.29, ...


Express the following recurring decimal as a rational number:

`2.3bar(5)`


Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then P2 R3 : S3 is equal to ______.


If pth, qth, and rth terms of an A.P. and G.P. are both a, b and c respectively, show that ab–c . bc – a . ca – b = 1


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 ______.


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


The sum of the infinite series `1 + 5/6 + 12/6^2 + 22/6^3 + 35/6^4 + 51/6^5 + 70/6^6 + ....` is equal to ______.


For an increasing G.P. a1, a2 , a3 ........., an, if a6 = 4a4, a9 – a7 = 192, then the value of `sum_(i = 1)^∞ 1/a_i` is ______.


The sum of infinite number of terms of a decreasing G.P. is 4 and the sum of the terms to m squares of its terms to infinity is `16/3`, then the G.P. is ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×