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

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 10 years. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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 10 years.

बेरीज
Advertisements

उत्तर

Since mosquitoes are growing at a rate of 10% and there were 200 mosquitoes, in the beginning, the number of mosquitoes in successive years form a G.P. with a = 200 and r = `1+10/100=11/10`

Number of mosquitoes after 10 years

= t11

= ar11–1

= `200(11/10)^10`

= 200 (1.1)10

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Sequences and Series - Exercise 2.1 [पृष्ठ २८]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 2 Sequences and Series
Exercise 2.1 | Q 14. (ii) | पृष्ठ २८

संबंधित प्रश्‍न

Which term of the following sequence:

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


Find the sum to indicated number of terms of the geometric progressions `sqrt7, sqrt21,3sqrt7`...n terms.


Evaluate `sum_(k=1)^11 (2+3^k )`


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


Find :

the 10th term of the G.P.

\[\sqrt{2}, \frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}, . . .\]


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

 

If \[\frac{a + bx}{a - bx} = \frac{b + cx}{b - cx} = \frac{c + dx}{c - dx}\] (x ≠ 0), then show that abc and d are in G.P.


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


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


Find the sum of the following geometric series:

`3/5 + 4/5^2 + 3/5^3 + 4/5^4 + ....` to 2n terms;


Find the sum of the following geometric series:

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


Find the sum of the following serie:

5 + 55 + 555 + ... to n terms;


Find the sum of the following series:

7 + 77 + 777 + ... to n terms;


If S1, S2, ..., Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ..., n respectively, then prove that S1 + S2 + 2S3 + 3S4 + ... (n − 1) Sn = 1n + 2n + 3n + ... + nn.


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 a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.


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

 (a + b + c + d)2 = (a + b)2 + 2 (b + c)2 + (c + d)2


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

(b + c) (b + d) = (c + a) (c + d)


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


In a G.P. if the (m + n)th term is p and (m − n)th term is q, then its mth term is 


Mark the correct alternative in the following question: 

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 p2R3 : S3 is equal to 


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

3, 4, 5, 6, …


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


For the G.P. if a = `2/3`, t6 = 162, find r.


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


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


For the following G.P.s, find Sn

3, 6, 12, 24, ...


Find: `sum_("r" = 1)^10 5 xx 3^"r"`


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

`2, 4/3, 8/9, 16/27, ...`


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

`-3, 1, (-1)/3, 1/9, ...`


Express the following recurring decimal as a rational number:

`0.bar(7)`


Express the following recurring decimal as a rational number:

`2.bar(4)`


Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.


Select the correct answer from the given alternative.

If for a G.P. `"t"_6/"t"_3 = 1458/54` then r = ?


Answer the following:

For a G.P. a = `4/3` and t7 = `243/1024`, find the value of r


In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is ______.


Let A1, A2, A3, .... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = `1/1296` and A2 + A4 = `7/36`, then the value of A6 + A8 + A10 is equal to ______. 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×