Advertisements
Advertisements
Question
The numbers 3, x, and x + 6 form are in G.P. Find nth term
Advertisements
Solution
When x = 6, nth term is given by
tn = arn–1, where a = 3, r = `"x"/3 = 6/3` = 2
∴ tn = 3(2)n–1
When x = – 3, nth term is given by
tn = arn–1, where a = 3, r = `"x"/3 = (-3)/3` = – 1
∴ tn = 3(– 1)n–1
Hence, nth term = 3(2)n–1 or 3(– 1)n–1.
APPEARS IN
RELATED QUESTIONS
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
For what values of x, the numbers `-2/7, x, -7/2` are in G.P?
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 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.
The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio `(3 + 2sqrt2) ":" (3 - 2sqrt2)`.
If 5th, 8th and 11th terms of a G.P. are p. q and s respectively, prove that q2 = ps.
Find the sum of the following series:
7 + 77 + 777 + ... to n terms;
How many terms of the G.P. 3, 3/2, 3/4, ... be taken together to make \[\frac{3069}{512}\] ?
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.
If S1, S2, S3 be respectively the sums of n, 2n, 3n terms of a G.P., then prove that \[S_1^2 + S_2^2\] = S1 (S2 + S3).
Express the recurring decimal 0.125125125 ... as a rational number.
Find the rational numbers having the following decimal expansion:
\[0 . \overline3\]
The sum of three numbers which are consecutive terms of an A.P. is 21. If the second number is reduced by 1 and the third is increased by 1, we obtain three consecutive terms of a G.P. Find the numbers.
If a, b, c, d are in G.P., prove that:
(a + b + c + d)2 = (a + b)2 + 2 (b + c)2 + (c + d)2
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.
If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is
For the G.P. if a = `2/3`, t6 = 162, find r.
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
The number of bacteria in a culture doubles every hour. If there were 50 bacteria originally in the culture, how many bacteria will be there at the end of 5th hour?
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.
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.
The numbers x − 6, 2x and x2 are in G.P. Find x
For the following G.P.s, find Sn
3, 6, 12, 24, ...
For the following G.P.s, find Sn.
p, q, `"q"^2/"p", "q"^3/"p"^2,` ...
The sum of an infinite G.P. is 5 and the sum of the squares of these terms is 15 find the G.P.
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.
Answer the following:
If for a G.P. first term is (27)2 and seventh term is (8)2, find S8
Answer the following:
If a, b, c are in G.P. and ax2 + 2bx + c = 0 and px2 + 2qx + r = 0 have common roots then verify that pb2 – 2qba + ra2 = 0
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 ______.
The third term of G.P. is 4. The product of its first 5 terms is ______.
The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252cm2. The length of the longest edge is ______.
For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to ______.
Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.
If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
Let A1, A2, A3, .... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = `1/1296` and A2 + A4 = `7/36`, then the value of A6 + A8 + A10 is equal to ______.
