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 3 years.

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 3 years.

योग
Advertisements

उत्तर

a = 200, r = `1 + 10/100 = 11/10`

Mosquitoes at the end of 1st year = `200 xx 11/10`

Number of mosquitoes after 3 years

= `200 xx 11/10 xx (11/10)^2`

= `200(11/10)^3`

= 200 (1.1)3

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

संबंधित प्रश्न

Which term of the following sequence:

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


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 a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.


Find the value of n so that  `(a^(n+1) + b^(n+1))/(a^n + b^n)` may be the geometric mean between a and b.


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


If f is a function satisfying f (x +y) = f(x) f(y) for all x, y ∈ N such that f(1) = 3 and `sum_(x = 1)^n` f(x) = 120, find the value of n.


Which term of the G.P. :

\[\sqrt{2}, \frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}, \frac{1}{4\sqrt{2}}, . . . \text { is }\frac{1}{512\sqrt{2}}?\]


Which term of the G.P. :

\[2, 2\sqrt{2}, 4, . . .\text {  is }128 ?\]


Find the 4th term from the end of the G.P.

\[\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, . . . , \frac{1}{4374}\]


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


The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.


The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.


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 \[\frac{1}{r^n}\].


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.


Find the sum of the following serie to infinity:

`2/5 + 3/5^2 +2/5^3 + 3/5^4 + ... ∞.`


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.


Express the recurring decimal 0.125125125 ... as a rational number.


If a, b, c are in G.P., prove that:

a (b2 + c2) = c (a2 + b2)


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 A1, A2 be two AM's and G1, G2 be two GM's between a and b, then find the value of \[\frac{A_1 + A_2}{G_1 G_2}\]


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


The two geometric means between the numbers 1 and 64 are 


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


Which term of the G.P. 5, 25, 125, 625, … is 510?


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:

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


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

`1/5, (-2)/5, 4/5, (-8)/5, 16/5, ...`


Express the following recurring decimal as a rational number:

`2.3bar(5)`


If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term


Find `sum_("r" = 0)^oo (-8)(-1/2)^"r"` 


Find : `sum_("n" = 1)^oo 0.4^"n"`


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


Select the correct answer from the given alternative.

Which term of the geometric progression 1, 2, 4, 8, ... is 2048


Answer the following:

Find the sum of the first 5 terms of the G.P. whose first term is 1 and common ratio is `2/3`


Answer the following:

If for a G.P. t3 = `1/3`, t6 = `1/81` find r


Answer the following:

Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.


Answer the following:

If p, q, r, s are in G.P., show that (p2 + q2 + r2) (q2 + r2 + s2) = (pq + qr + rs)2   


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×