Advertisements
Advertisements
Question
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Advertisements
Solution
Let the first term of the geometric progression = a
Common ratio = 2
12th term = a × 212−1 = 211 a
8th term = a × 28−1 = a × 27 = 128a
Given: 8th term = 192
∴ 128a = 192
or a = `192/128 = 3/2`
∴ 12th term = `1^11 xx 3/2`
= `2^10 xx 3`
= 1024 × 3
= 3072
APPEARS IN
RELATED QUESTIONS
If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.
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, ...
Find :
nth term of the G.P.
\[\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3\sqrt{3}}, . . .\]
If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.
If the pth and qth terms of a G.P. are q and p, respectively, then show that (p + q)th term is \[\left( \frac{q^p}{p^q} \right)^\frac{1}{p - q}\].
Find three numbers in G.P. whose sum is 65 and whose product is 3375.
Find the sum of the following geometric progression:
1, −1/2, 1/4, −1/8, ... to 9 terms;
Find the sum of the following geometric series:
`3/5 + 4/5^2 + 3/5^3 + 4/5^4 + ....` to 2n terms;
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 ratio of the sum of the first three terms to that of the first 6 terms of a G.P. is 125 : 152. Find the common ratio.
Find the sum of the following serie to infinity:
8 + \[4\sqrt{2}\] + 4 + ... ∞
Find the sum of the following series to infinity:
`1/3+1/5^2 +1/3^3+1/5^4 + 1/3^5 + 1/56+ ...infty`
If a, b, c are in G.P., prove that \[\frac{1}{\log_a m}, \frac{1}{\log_b m}, \frac{1}{\log_c m}\] are in A.P.
Find k such that k + 9, k − 6 and 4 form three consecutive terms of a G.P.
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. and a, b, d are in G.P., show that a, (a − b), (d − c) are in G.P.
Find the geometric means of the following pairs of number:
2 and 8
If pth, qth and rth terms of a G.P. re x, y, z respectively, then write the value of xq − r yr − pzp − q.
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
If pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is
The fifth term of a G.P. is x, eighth term of a G.P. is y and eleventh term of a G.P. is z verify whether y2 = xz
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 3 years.
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]
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:
`0.bar(7)`
Express the following recurring decimal as a rational number:
`2.3bar(5)`
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 perimeters of all the squares
Select the correct answer from the given alternative.
The common ratio for the G.P. 0.12, 0.24, 0.48, is –
Select the correct answer from the given alternative.
Which of the following is not true, where A, G, H are the AM, GM, HM of a and b respectively. (a, b > 0)
Answer the following:
In a G.P., the fourth term is 48 and the eighth term is 768. Find the tenth term
Answer the following:
Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...
Answer the following:
If for a G.P. first term is (27)2 and seventh term is (8)2, find S8
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 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 ______.
The sum of the infinite series `1 + 5/6 + 12/6^2 + 22/6^3 + 35/6^4 + 51/6^5 + 70/6^6 + ....` is equal to ______.
