हिंदी

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.

योग

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Sequences and Series - Exercise 2.1 [पृष्ठ २८]

APPEARS IN

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

संबंधित प्रश्न

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.


Find the sum of the products of the corresponding terms of the sequences `2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2`


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.


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

−2/3, −6, −54, ...


Find:
the ninth term of the G.P. 1, 4, 16, 64, ...


Find :

the 8th term of the G.P. 0.3, 0.06, 0.012, ...


The product of three numbers in G.P. is 125 and the sum of their products taken in pairs is \[87\frac{1}{2}\] . Find them.


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:

 0.15 + 0.015 + 0.0015 + ... to 8 terms;


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:

x3, x5, x7, ... to n terms


Evaluate the following:

\[\sum^{10}_{n = 2} 4^n\]


The sum of n terms of the G.P. 3, 6, 12, ... is 381. Find the value of n.


How many terms of the G.P. 3, \[\frac{3}{2}, \frac{3}{4}\] ..... are needed to give the sum \[\frac{3069}{512}\] ?


A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying the odd places. Find the common ratio of the G.P.


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


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

a2 + b2, ab + bc, b2 + c2


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.


If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is 


The fractional value of 2.357 is 


If abc are in G.P. and xy are AM's between ab and b,c respectively, then 


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


The two geometric means between the numbers 1 and 64 are 


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


If S, P, R are the sum, product, and sum of the reciprocals of n terms of a G.P. respectively, then verify that `["S"/"R"]^"n"` = P


If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n – S2n) = (S2n – Sn)2.


The value of a house appreciates 5% per year. How much is the house worth after 6 years if its current worth is ₹ 15 Lac. [Given: (1.05)5 = 1.28, (1.05)6 = 1.34]


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

`1/2, 1/4, 1/8, 1/16,...`


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


The midpoints of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the areas of all the squares


A ball is dropped from a height of 10m. It bounces to a height of 6m, then 3.6m and so on. Find the total distance travelled by the ball


Answer the following:

For a sequence Sn = 4(7n – 1) verify that the sequence is a G.P.


Answer the following:

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


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


Let `{a_n}_(n = 0)^∞` be a sequence such that a0 = a1 = 0 and an+2 = 2an+1 – an + 1 for all n ≥ 0. Then, `sum_(n = 2)^∞ a^n/7^n` is equal to ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×