हिंदी

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

Advertisements
Advertisements

प्रश्न

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

योग

उत्तर

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

2xx-6=x22x

∴ 4x2 = x2(x – 6)

∴ 4 = x – 6   ...[∵ x2 ≠ 0]

∴ x = 10

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Sequences and Series - Exercise 2.1 [पृष्ठ २८]

APPEARS IN

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

संबंधित प्रश्न

Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).


The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.


Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.


Find the sum to n terms of the sequence, 8, 88, 888, 8888… .


Find:

the 10th term of the G.P.

34,12,13,29,...

 


Find : 

nth term of the G.P.

3,13,133,...


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.


The 4th term of a G.P. is square of its second term, and the first term is − 3. Find its 7th term.


If a, b, c, d and p are different real numbers such that:
(a2 + b2 + c2) p2 − 2 (ab + bc + cd) p + (b2 + c2 + d2) ≤ 0, then show that a, b, c and d are in G.P.


Find the sum of the following geometric progression:

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


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, ..., Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ..., n respectively, then prove that S1 + S2 + 2S3 + 3S4 + ... (n − 1) Sn = 1n + 2n + 3n + ... + nn.


If a, b, c are in G.P., prove that:

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


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

a3, b3, c3


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

1a2+b2,1b2c2,1c2+d2 are in G . P .


If a, b, c are in A.P., b,c,d are in G.P. and 1c,1d,1e are in A.P., prove that a, c,e are in G.P.


Find the geometric means of the following pairs of number:

2 and 8


If a = 1 + b + b2 + b3 + ... to ∞, then write b in terms of a.


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


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


A ball is dropped from a height of 80 ft. The ball is such that it rebounds (34)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?


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

p, q, q2p,q3p2, ...


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


If S, P, R are the sum, product, and sum of the reciprocals of n terms of a G.P. respectively, then verify that [SR]n = P


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.


Express the following recurring decimal as a rational number:

2.35¯


Select the correct answer from the given alternative.

The sum of 3 terms of a G.P. is 214 and their product is 1 then the common ratio is –


Answer the following:

For a G.P. a = 43 and t7 = 2431024, find the value of r


Answer the following:

Find three numbers in G.P. such that their sum is 35 and their product is 1000


Answer the following:

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


Answer the following:

Find r=1n(23)r


For a, b, c to be in G.P. the value of a-bb-c is equal to ______.


The sum of the infinite series 1+56+1262+2263+3564+5165+7066+.... is equal to ______.


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.