Advertisements
Advertisements
Question
Check whether the following sequence is G.P. If so, write tn.
7, 14, 21, 28, …
Advertisements
Solution
7, 14, 21, 28, …
t1 = 7, t2 = 14, t3 = 21, t4 = 28
Here, `"t"_2/"t"_1` = 2, `"t"_3/"t"_2 = 3/2`, `"t"_4/"t"_3 = 4/3`
∵ `"t"_2/"t"_1 ≠ "t"_3/"t"_2 ≠ "t"_4/"t"_3`
∴ the sequence is not a Geometric progression.
APPEARS IN
RELATED QUESTIONS
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Find the sum to indicated number of terms of the geometric progressions `sqrt7, sqrt21,3sqrt7`...n terms.
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.
If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that `a^(q - r) b^(r-p) c^(p-q) = 1`.
If a, b, c and d are in G.P. show that (a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)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.: `sqrt3, 3, 3sqrt3`, ... is 729?
Find three numbers in G.P. whose sum is 65 and whose product is 3375.
The sum of first three terms of a G.P. is \[\frac{39}{10}\] and their product is 1. Find the common ratio and the terms.
The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.
Find the sum of the following geometric series:
\[\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} + . . .\text { to 8 terms };\]
Find the sum of the following geometric series:
`3/5 + 4/5^2 + 3/5^3 + 4/5^4 + ....` to 2n terms;
Find the sum of the following geometric series:
\[\frac{a}{1 + i} + \frac{a}{(1 + i )^2} + \frac{a}{(1 + i )^3} + . . . + \frac{a}{(1 + i )^n} .\]
Find the sum of the following series:
7 + 77 + 777 + ... to n 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.
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)th to (2n)th term is \[\frac{1}{r^n}\].
Find the sum of the following serie to infinity:
8 + \[4\sqrt{2}\] + 4 + ... ∞
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 are in G.P., prove that the following is also in G.P.:
a2, b2, c2
If xa = xb/2 zb/2 = zc, then prove that \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
If A1, A2 be two AM's and G1, G2 be two GM's between a and b, then find the value of \[\frac{A_1 + A_2}{G_1 G_2}\]
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 value of 91/3 . 91/9 . 91/27 ... upto inf, is
For the G.P. if a = `7/243`, r = 3 find t6.
For the G.P. if a = `2/3`, t6 = 162, find r.
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.
The numbers x − 6, 2x and x2 are in G.P. Find x
For the following G.P.s, find Sn.
`sqrt(5)`, −5, `5sqrt(5)`, −25, ...
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:
9, 8.1, 7.29, ...
Express the following recurring decimal as a rational number:
`0.bar(7)`
Find `sum_("r" = 0)^oo (-8)(-1/2)^"r"`
A ball is dropped from a height of 10m. It bounces to a height of 6m, then 3.6m and so on. Find the total distance travelled by the ball
The sum of 3 terms of a G.P. is `21/4` and their product is 1 then the common ratio 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:
Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...
Answer the following:
For a G.P. if t2 = 7, t4 = 1575 find a
At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was Rs 1250, find the value at the end of 5 years.
