मराठी

Find : the 8th Term of the G.P. 0.3, 0.06, 0.012, ... - Mathematics

Advertisements
Advertisements

प्रश्न

Find :

the 8th term of the G.P. 0.3, 0.06, 0.012, ...

उत्तर

Here,

 First term ,a=0.3

 Common ratio ,r=a2a1=0.060.3=0.2

8th term =a8=ar(81)=0.3(0.2)7

 Thus, the 8th term of the given GP is 0.3(0.2)7.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 20: Geometric Progression - Exercise 20.1 [पृष्ठ १०]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 20 Geometric Progression
Exercise 20.1 | Q 3.3 | पृष्ठ १०

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Show that the products of the corresponding terms of the sequences a, ar, ar2, …arn – 1 and A, AR, AR2, … ARn-1 form a G.P, and find the common ratio


If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P.


Show that one of the following progression is a G.P. Also, find the common ratio in case:

4, −2, 1, −1/2, ...


Show that the sequence <an>, defined by an = 23n, n ϵ N is a G.P.


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

227,29,23,...,162

If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.


In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.


Find the sum of the following geometric progression:

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


Find the sum of the following geometric series:

1, −a, a2, −a3, ....to n terms (a ≠ 1)


Evaluate the following:

n=2104n


How many terms of the G.P. 3, 3/2, 3/4, ... be taken together to make 3069512 ?


The sum of n terms of the G.P. 3, 6, 12, ... is 381. Find the value of n.


If S denotes the sum of an infinite G.P. S1 denotes the sum of the squares of its terms, then prove that the first term and common ratio are respectively

2SS1S2+S1 and S2S1S2+S1


The sum of three numbers which are consecutive terms of an A.P. is 21. If the second number is reduced by 1 and the third is increased by 1, we obtain three consecutive terms of a G.P. Find the numbers.


If a, b, c are in G.P., prove that:

a2b2c2(1a3+1b3+1c3)=a3+b3+c3


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 abc are in G.P. and xy are AM's between ab and b,c respectively, then 


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


Mark the correct alternative in the following question: 

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 p2R3 : S3 is equal to 


For the G.P. if a = 7243, r = 3 find t6.


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.


For the following G.P.s, find Sn

0.7, 0.07, 0.007, .....


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

5, −5, 55, −25, ...


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


For a sequence, if Sn = 2(3n –1), find the nth term, hence show that the sequence is a G.P.


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

12,14,18,116,...


Express the following recurring decimal as a rational number:

0.7¯


If the common ratio of a G.P. is 23 and sum to infinity is 12. Find the first term


Find GM of two positive numbers whose A.M. and H.M. are 75 and 48


Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.


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:

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


If e(cos2x+cos4x+cos6x+...)loge2 satisfies the equation t2 – 9t + 8 = 0, then the value of 2sinxsinx+3cosx(0<x,<π2) is ______.


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 ______.


For an increasing G.P. a1, a2 , a3 ........., an, if a6 = 4a4, a9 – a7 = 192, then the value of i=11ai is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.