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.
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
APPEARS IN
संबंधित प्रश्न
Find the 20th and nthterms of the G.P. `5/2, 5/4 , 5/8,...`
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 a, b, c are in A.P,; b, c, d are in G.P and ` 1/c, 1/d,1/e` are in A.P. prove that a, c, e are in G.P.
Find :
the 12th term of the G.P.
\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]
If 5th, 8th and 11th terms of a G.P. are p. q and s respectively, prove that q2 = ps.
The 4th term of a G.P. is square of its second term, and the first term is − 3. Find its 7th term.
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.
The sum of three numbers in G.P. is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers are in A.P. Find the numbers.
The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.
Find the sum of the following geometric progression:
4, 2, 1, 1/2 ... to 10 terms.
Evaluate the following:
\[\sum^n_{k = 1} ( 2^k + 3^{k - 1} )\]
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 \[39 + 13\sqrt{3}\] ?
The common ratio of a G.P. is 3 and the last term is 486. If the sum of these terms be 728, find the first term.
The 4th and 7th terms of a G.P. are \[\frac{1}{27} \text { and } \frac{1}{729}\] respectively. Find the sum of n terms of the G.P.
How many terms of the G.P. 3, \[\frac{3}{2}, \frac{3}{4}\] ..... are needed to give the sum \[\frac{3069}{512}\] ?
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.
The sum of first two terms of an infinite G.P. is 5 and each term is three times the sum of the succeeding terms. Find the G.P.
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
\[\frac{2S S_1}{S^2 + S_1}\text { and } \frac{S^2 - S_1}{S^2 + S_1}\]
If a, b, c are in G.P., prove that log a, log b, log c are in A.P.
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
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 A.P., b,c,d are in G.P. and \[\frac{1}{c}, \frac{1}{d}, \frac{1}{e}\] are in A.P., prove that a, c,e are in G.P.
If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is \[\frac{9}{2}\], then write its first term and common difference.
If the first term of a G.P. a1, a2, a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is
The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then its first term is ______.
For the G.P. if a = `2/3`, t6 = 162, find r.
The numbers 3, x, and x + 6 form are in G.P. Find 20th term.
The numbers 3, x, and x + 6 form are in G.P. Find nth term
For the following G.P.s, find Sn.
p, q, `"q"^2/"p", "q"^3/"p"^2,` ...
Find the sum to n terms of the sequence.
0.2, 0.02, 0.002, ...
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.
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 GM of two positive numbers whose A.M. and H.M. are 75 and 48
Answer the following:
For a sequence , if tn = `(5^("n" - 2))/(7^("n" - 3))`, verify whether the sequence is a G.P. If it is a G.P., find its first term and the common ratio.
Answer the following:
Find three numbers in G.P. such that their sum is 35 and their product is 1000
In a G.P. of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P. is ______.
If pth, qth, and rth terms of an A.P. and G.P. are both a, b and c respectively, show that ab–c . bc – a . ca – b = 1
