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 n years.
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 n years
= `200 xx 11/10 xx (11/10)^2`
= `200(11/10)^"n"`
= After n years, = 200 (1.1)n
APPEARS IN
संबंधित प्रश्न
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Which term of the following sequence:
`1/3, 1/9, 1/27`, ...., is `1/19683`?
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`
Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
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)`.
Show that one of the following progression is a G.P. Also, find the common ratio in case:1/2, 1/3, 2/9, 4/27, ...
Find :
the 8th term of the G.P. 0.3, 0.06, 0.012, ...
Which term of the progression 0.004, 0.02, 0.1, ... is 12.5?
If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.
If a, b, c, d and p are different real numbers such that:
(a2 + b2 + c2) p2 − 2 (ab + bc + cd) p + (b2 + c2 + d2) ≤ 0, then show that a, b, c and d are in G.P.
Find three numbers in G.P. whose sum is 65 and whose product is 3375.
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 the sum of the following geometric series:
1, −a, a2, −a3, ....to n terms (a ≠ 1)
Evaluate the following:
\[\sum^{11}_{n = 1} (2 + 3^n )\]
Find the sum of the following series:
7 + 77 + 777 + ... to n terms;
How many terms of the sequence \[\sqrt{3}, 3, 3\sqrt{3},\] ... must be taken to make the sum \[39 + 13\sqrt{3}\] ?
Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.
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, d are in G.P., prove that:
(a2 + b2), (b2 + c2), (c2 + d2) are in G.P.
If a, b, c are in G.P., then prove that:
If xa = xb/2 zb/2 = zc, then prove that \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio `(3+2sqrt2):(3-2sqrt2)`.
If logxa, ax/2 and logb x are in G.P., then write the value of x.
If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms, then its first term is
If a, b, c are in G.P. and x, y are AM's between a, b and b,c respectively, then
If x is positive, the sum to infinity of the series \[\frac{1}{1 + x} - \frac{1 - x}{(1 + x )^2} + \frac{(1 - x )^2}{(1 + x )^3} - \frac{(1 - x )^3}{(1 + x )^4} + . . . . . . is\]
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
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
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
The numbers x − 6, 2x and x2 are in G.P. Find 1st term
The numbers x − 6, 2x and x2 are in G.P. Find nth term
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, ...`
Select the correct answer from the given alternative.
The common ratio for the G.P. 0.12, 0.24, 0.48, is –
Answer the following:
For a sequence Sn = 4(7n – 1) verify that the sequence is a G.P.
If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.
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 ______.
If the sum of an infinite GP a, ar, ar2, ar3, ...... . is 15 and the sum of the squares of its each term is 150, then the sum of ar2, ar4, ar6, .... is ______.
