Advertisements
Advertisements
Question
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.
Solution
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
RELATED QUESTIONS
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
For what values of x, the numbers `-2/7, x, -7/2` are in G.P?
Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015,…
Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).
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 sum of the products of the corresponding terms of the sequences `2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2`
If a, b, c and d are in G.P. show that (a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2 .
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.
Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn
Show that one of the following progression is a G.P. Also, find the common ratio in case:
4, −2, 1, −1/2, ...
Show that one of the following progression is a G.P. Also, find the common ratio in case:
−2/3, −6, −54, ...
Which term of the G.P. :
\[2, 2\sqrt{2}, 4, . . .\text { is }128 ?\]
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.
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.
Find the sum :
\[\sum^{10}_{n = 1} \left[ \left( \frac{1}{2} \right)^{n - 1} + \left( \frac{1}{5} \right)^{n + 1} \right] .\]
If a and b are the roots of x2 − 3x + p = 0 and c, d are the roots x2 − 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q − p) = 17 : 15.
If a, b, c are in G.P., prove that log a, log b, log c are in A.P.
If a, b, c, d are in G.P., prove that:
(b + c) (b + d) = (c + a) (c + d)
If a, b, c are in G.P., then prove that:
If \[\frac{1}{a + b}, \frac{1}{2b}, \frac{1}{b + c}\] are three consecutive terms of an A.P., prove that a, b, c are the three consecutive terms of a G.P.
If a, b, c are in G.P. and x, y are AM's between a, b and b,c respectively, then
If p, q be two A.M.'s and G be one G.M. between two numbers, then G2 =
For the G.P. if r = − 3 and t6 = 1701, find a.
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
Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.
The numbers 3, x, and x + 6 form are in G.P. Find nth term
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.
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.
Find: `sum_("r" = 1)^10 5 xx 3^"r"`
If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)5 = 1.47]
Express the following recurring decimal as a rational number:
`2.bar(4)`
Select the correct answer from the given alternative.
Sum to infinity of a G.P. 5, `-5/2, 5/4, -5/8, 5/16,...` is –
Answer the following:
Find `sum_("r" = 1)^"n" (2/3)^"r"`
Answer the following:
Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.
If a, b, c, d are four distinct positive quantities in G.P., then show that a + d > b + c
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 ______.
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
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 ______.
If 0 < x, y, a, b < 1, then the sum of the infinite terms of the series `sqrt(x)(sqrt(a) + sqrt(x)) + sqrt(x)(sqrt(ab) + sqrt(xy)) + sqrt(x)(bsqrt(a) + ysqrt(x)) + ...` is ______.
