English

Check whether the following sequence is G.P. If so, write tn. 3, 4, 5, 6, … - Mathematics and Statistics

Advertisements
Advertisements

Question

Check whether the following sequence is G.P. If so, write tn.

3, 4, 5, 6, …

Sum

Solution

Here, t1 = 3, t2 = 4, t3 = 5, t4 = 6, ...

∴ `"t"_2/"t"_1 = 4/3, "t"_3/"t"_2 = 5/4, "t"_4/"t"_3 = 6/5`

∵ `"t"_2/"t"_1 ≠ "t"_3/"t"_2 ≠ "t"_4/"t"_3`

∴ given sequence is not a geometric progression.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Sequences and Series - Exercise 2.1 [Page 27]

APPEARS IN

RELATED QUESTIONS

Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.


Find the value of n so that  `(a^(n+1) + b^(n+1))/(a^n + b^n)` may be the geometric mean between a and b.


A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.


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


Which term of the G.P. :

\[\sqrt{3}, 3, 3\sqrt{3}, . . . \text { is } 729 ?\]


Which term of the G.P. :

\[\frac{1}{3}, \frac{1}{9}, \frac{1}{27} . . \text { . is } \frac{1}{19683} ?\]


Find the 4th term from the end of the G.P.

\[\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, . . . , \frac{1}{4374}\]


The sum of first three terms of a G.P. is 13/12 and their product is − 1. Find the G.P.


Find the sum of the following geometric series:

 0.15 + 0.015 + 0.0015 + ... to 8 terms;


Find the sum of the following geometric series:

\[\sqrt{7}, \sqrt{21}, 3\sqrt{7}, . . .\text {  to n terms }\]


Find the sum of the following serie:

5 + 55 + 555 + ... to n terms;


How many terms of the sequence \[\sqrt{3}, 3, 3\sqrt{3},\]  ... must be taken to make the sum \[39 + 13\sqrt{3}\] ?


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.


If a, b, c are in G.P., prove that:

\[a^2 b^2 c^2 \left( \frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{c^3} \right) = a^3 + b^3 + c^3\]


If a, b, c are in G.P., prove that the following is also in G.P.:

a2 + b2, ab + bc, b2 + c2


If a, b, c, d are in G.P., prove that:

(a2 + b2), (b2 + c2), (c2 + d2) are in G.P.


If pth, qth and rth terms of an A.P. and G.P. are both a, b and c respectively, show that \[a^{b - c} b^{c - a} c^{a - b} = 1\]


Find the geometric means of the following pairs of number:

−8 and −2


The value of 91/3 . 91/9 . 91/27 ... upto inf, is 


The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 92. The common ratio of the original G.P. is 


If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is


Given that x > 0, the sum \[\sum^\infty_{n = 1} \left( \frac{x}{x + 1} \right)^{n - 1}\] equals 


In a G.P. if the (m + n)th term is p and (m − n)th term is q, then its mth term is 


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


For the following G.P.s, find Sn

3, 6, 12, 24, ...


For the following G.P.s, find Sn

0.7, 0.07, 0.007, .....


For a G.P. if a = 2, r = 3, Sn = 242 find n


Find: `sum_("r" = 1)^10(3 xx 2^"r")`


The value of a house appreciates 5% per year. How much is the house worth after 6 years if its current worth is ₹ 15 Lac. [Given: (1.05)5 = 1.28, (1.05)6 = 1.34]


Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`1/2, 1/4, 1/8, 1/16,...`


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:

Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`


If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.


Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then P2 R3 : S3 is equal to ______.


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


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×