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

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?

Advertisements
Advertisements

प्रश्न

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?

बेरीज
Advertisements

उत्तर

a = 50 

r = 2 

n = 5

we have, 

tn = `a*r^((n - 1))`

t5 = `(50)*(2)^(5-1)`

= 50 × (2)4

= 50 × 16

t5 = 800

 After 5th hour 800 bacterias will be there in culture.

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

APPEARS IN

संबंधित प्रश्‍न

Find the 20th and nthterms of the G.P. `5/2, 5/4 , 5/8,...`


Which term of the following sequence:

`sqrt3, 3, 3sqrt3`, .... is 729?


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?


The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.


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`.


If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.


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


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


Find three numbers in G.P. whose sum is 65 and whose product is 3375.


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


Find the sum of the following geometric series:

\[\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . \text { to 5 terms };\]


The ratio of the sum of the first three terms to that of the first 6 terms of a G.P. is 125 : 152. Find the common ratio.


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).


A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.


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`


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


Find the rational numbers having the following decimal expansion: 

\[0 . \overline3\]


If a, b, c are in G.P., prove that log a, log b, log c are in A.P.


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

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


If pth, qth and rth terms of an A.P. and G.P. are both a, b and c respectively, show that \[a^{b - c} b^{c - a} c^{a - b} = 1\]


Insert 5 geometric means between \[\frac{32}{9}\text{and}\frac{81}{2}\] .


The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio `(3+2sqrt2):(3-2sqrt2)`.


If the fifth term of a G.P. is 2, then write the product of its 9 terms.


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


If a = 1 + b + b2 + b3 + ... to ∞, then write b in terms of a.


The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 92. The common ratio of the original G.P. is 


Let x be the A.M. and y, z be two G.M.s between two positive numbers. Then, \[\frac{y^3 + z^3}{xyz}\]  is equal to 


If for a sequence, tn = `(5^("n"-3))/(2^("n"-3))`, show that the sequence is a G.P. Find its first term and the common ratio


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


For a G.P. sum of first 3 terms is 125 and sum of next 3 terms is 27, find the value of r


Answer the following:

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


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 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))`


For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to ______.


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 ______.


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×