English

The numbers 3, x, and x + 6 form are in G.P. Find 20th term. - Mathematics and Statistics

Advertisements
Advertisements

Question

The numbers 3, x, and x + 6 form are in G.P. Find 20th term.

Sum

Solution

r = `6/3` = 2 or r = `(-3)/3` = – 1

tn = arn–1

∴ t20 = 3(219) or t20 = 3(– 1)19

∴ t20 = 3(219) or t20 = – 3

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Sequences and Series - Exercise 2.1 [Page 28]

APPEARS IN

RELATED QUESTIONS

The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.


Which term of the following sequence:

`sqrt3, 3, 3sqrt3`, .... is 729?


Which term of the following sequence:

`1/3, 1/9, 1/27`, ...., is `1/19683`?


For what values of x, the numbers  `-2/7, x, -7/2` are in G.P?


The sum of first three terms of a G.P. is  `39/10` and their product is 1. Find the common ratio and the terms.


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


If a and b are the roots of are roots of x2 – 3x + p = 0 , and c, d are roots of x2 – 12x + q = 0, where a, b, c, d, form a G.P. Prove that (q + p): (q – p) = 17 : 15.


Show that the sequence <an>, defined by an = \[\frac{2}{3^n}\], n ϵ N is a G.P.


Which term of the progression 18, −12, 8, ... is \[\frac{512}{729}\] ?

 

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 the sum of the following geometric progression:

2, 6, 18, ... to 7 terms;


Find the sum of the following geometric series:

\[\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} + . . .\text { to 8  terms };\]


Evaluate the following:

\[\sum^{10}_{n = 2} 4^n\]


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


The ratio of the sum of first three terms is to that of first 6 terms of a G.P. is 125 : 152. Find the common ratio.


Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.


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

\[\frac{1}{a^2 + b^2}, \frac{1}{b^2 - c^2}, \frac{1}{c^2 + d^2} \text { are in G . P } .\]


If xa = xb/2 zb/2 = zc, then prove that \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.

  

Find the geometric means of the following pairs of number:

a3b and ab3


If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms, then its first term is 


The nth term of a G.P. is 128 and the sum of its n terms  is 225. If its common ratio is 2, then its first term is


If x is positive, the sum to infinity of the series \[\frac{1}{1 + x} - \frac{1 - x}{(1 + x )^2} + \frac{(1 - x )^2}{(1 + x )^3} - \frac{(1 - x )^3}{(1 + x )^4} + . . . . . . is\]


If x = (43) (46) (46) (49) .... (43x) = (0.0625)−54, the value of x is 


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

`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...


For what values of x, the terms `4/3`, x, `4/27` are in G.P.?


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 1st term


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.


If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term


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 areas of all the squares


Answer the following:

If pth, qth and rth terms of a G.P. are x, y, z respectively. Find the value of xq–r .yr–p .zp–q


Answer the following:

Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.


If a, b, c, d are four distinct positive quantities in G.P., then show that a + d > b + c


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 ______.


If 0 < x, y, a, b < 1, then the sum of the infinite terms of the series `sqrt(x)(sqrt(a) + sqrt(x)) + sqrt(x)(sqrt(ab) + sqrt(xy)) + sqrt(x)(bsqrt(a) + ysqrt(x)) + ...` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×