मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

The numbers x − 6, 2x and x2 are in G.P. Find nth term - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

The numbers x − 6, 2x and x2 are in G.P. Find nth term

बेरीज
Advertisements

उत्तर

nth term = arn−1, where a = 4, r = `x^2/(2x)` = `100/20` = 5

= 4(5)n−1

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Sequences and Series - Exercise 2.1 [पृष्ठ २८]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 2 Sequences and Series
Exercise 2.1 | Q 15. (iii) | पृष्ठ २८

संबंधित प्रश्‍न

Evaluate `sum_(k=1)^11 (2+3^k )`


If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.


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 `1/r^n`.


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


Find:
the ninth term of the G.P. 1, 4, 16, 64, ...


Which term of the G.P.: `sqrt3, 3, 3sqrt3`, ... is 729?


If the pth and qth terms of a G.P. are q and p, respectively, then show that (p + q)th term is \[\left( \frac{q^p}{p^q} \right)^\frac{1}{p - q}\].


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


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.


How many terms of the G.P. `3, 3/2, 3/4` ..... are needed to give the sum `3069/512`?


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


Find the sum of the following series to infinity:

10 − 9 + 8.1 − 7.29 + ... ∞


Show that in an infinite G.P. with common ratio r (|r| < 1), each term bears a constant ratio to the sum of all terms that follow it.


The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an A.P. Find the numbers.


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, 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 a, b, c are three distinct real numbers in G.P. and a + b + c = xb, then prove that either x< −1 or x > 3.


Insert 5 geometric means between 16 and \[\frac{1}{4}\] .


Find the geometric means of the following pairs of number:

a3b and ab3


If (p + q)th and (p − q)th terms of a G.P. are m and n respectively, then write is pth term.


If pth, qth and rth terms of a G.P. re x, y, z respectively, then write the value of xq − r yr − pzp − q.

 

 

 


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


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


The two geometric means between the numbers 1 and 64 are 


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


For the G.P. if a = `2/3`, t6 = 162, find r.


Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.


The fifth term of a G.P. is x, eighth term of a G.P. is y and eleventh term of a G.P. is z verify whether y2 = xz


For the following G.P.s, find Sn.

`sqrt(5)`, −5, `5sqrt(5)`, −25, ...


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,...`


Express the following recurring decimal as a rational number:

`51.0bar(2)`


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


If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by `18/5`, find the numbers.


Answer the following:

For a G.P. if t2 = 7, t4 = 1575 find a


Answer the following:

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


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


Answer the following:

If p, q, r, s are in G.P., show that (p2 + q2 + r2) (q2 + r2 + s2) = (pq + qr + rs)2   


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×