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
Which term of the following sequence:
`2, 2sqrt2, 4,.... is 128`
Find the sum to indicated number of terms of the geometric progressions `sqrt7, sqrt21,3sqrt7`...n terms.
Find the sum to indicated number of terms in the geometric progressions x3, x5, x7, ... n terms (if x ≠ ± 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.
Show that the products of the corresponding terms of the sequences a, ar, ar2, …arn – 1 and A, AR, AR2, … `AR^(n-1)` form a G.P, and find the common ratio
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 some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
The 4th term of a G.P. is square of its second term, and the first term is − 3. Find its 7th term.
The sum of first three terms of a G.P. is 13/12 and their product is − 1. 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 of the following geometric progression:
2, 6, 18, ... to 7 terms;
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.
Find the sum of the following series to infinity:
10 − 9 + 8.1 − 7.29 + ... ∞
If Sp denotes the sum of the series 1 + rp + r2p + ... to ∞ and sp the sum of the series 1 − rp + r2p − ... to ∞, prove that Sp + sp = 2 . S2p.
Find the rational numbers having the following decimal expansion:
\[3 . 5\overline 2\]
One side of an equilateral triangle is 18 cm. The mid-points of its sides are joined to form another triangle whose mid-points, in turn, are joined to form still another triangle. The process is continued indefinitely. Find the sum of the (i) perimeters of all the triangles. (ii) areas of all triangles.
If a, b, c are in G.P., prove that log a, log b, log c are in A.P.
Three numbers are in A.P. and their sum is 15. If 1, 3, 9 be added to them respectively, they form a G.P. Find the numbers.
If a, b, c, d are in G.P., prove that:
\[\frac{1}{a^2 + b^2}, \frac{1}{b^2 - c^2}, \frac{1}{c^2 + d^2} \text { are in G . P } .\]
Write the product of n geometric means between two numbers a and b.
If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is
If a, b, c are in G.P. and x, y are AM's between a, b and b,c respectively, then
The two geometric means between the numbers 1 and 64 are
A ball is dropped from a height of 80 ft. The ball is such that it rebounds `(3/4)^"th"` of the height it has fallen. How high does the ball rebound on 6th bounce? How high does the ball rebound on nth bounce?
The numbers x − 6, 2x and x2 are in G.P. Find x
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.
Find: `sum_("r" = 1)^10 5 xx 3^"r"`
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:
`-3, 1, (-1)/3, 1/9, ...`
Express the following recurring decimal as a rational number:
`2.bar(4)`
If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term
The sum of an infinite G.P. is 5 and the sum of the squares of these terms is 15 find the G.P.
Find : `sum_("r" = 1)^oo 4(0.5)^"r"`
Find : `sum_("n" = 1)^oo 0.4^"n"`
Select the correct answer from the given alternative.
The common ratio for the G.P. 0.12, 0.24, 0.48, is –
For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to ______.
If the sum of an infinite GP a, ar, ar2, ar3, ...... . is 15 and the sum of the squares of its each term is 150, then the sum of ar2, ar4, ar6, .... is ______.
If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
