मराठी

Find the Sum of the Following Geometric Series: X3, X5, X7, ... to N Terms - Mathematics

Advertisements
Advertisements

प्रश्न

Find the sum of the following geometric series:

x3, x5, x7, ... to n terms

बेरीज
Advertisements

उत्तर

The given G.P. is  x3, x5, x7 ........

Here, a = x3 and r = x

`"S"_"n" = (a(1 - r^n))/(1 - r)`

= `(x^3[1 - (x^2)^n])/(1 - x^2)`

= `(x^3(1 - x^(2n)))/(1 - x^2)`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 20: Geometric Progression - Exercise 20.3 [पृष्ठ २७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 20 Geometric Progression
Exercise 20.3 | Q 2.8 | पृष्ठ २७

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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


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

\[\frac{2}{27}, \frac{2}{9}, \frac{2}{3}, . . . , 162\]

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

 

The product of three numbers in G.P. is 125 and the sum of their products taken in pairs is \[87\frac{1}{2}\] . Find them.


The sum of three numbers in G.P. is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers are in A.P. Find the numbers.


Find the sum of the following geometric series:

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


Find the sum of the following series:

0.5 + 0.55 + 0.555 + ... to n terms.


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


Find the sum :

\[\sum^{10}_{n = 1} \left[ \left( \frac{1}{2} \right)^{n - 1} + \left( \frac{1}{5} \right)^{n + 1} \right] .\]


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).


Find the sum of the following serie to infinity:

\[1 - \frac{1}{3} + \frac{1}{3^2} - \frac{1}{3^3} + \frac{1}{3^4} + . . . \infty\]


Find the sum of the following serie to infinity:

8 +  \[4\sqrt{2}\] + 4 + ... ∞


The sum of three numbers a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.


If a, b, c are in G.P., prove that:

a (b2 + c2) = c (a2 + b2)


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

\[\frac{ab - cd}{b^2 - c^2} = \frac{a + c}{b}\]


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

\[\frac{a^2 + ab + b^2}{bc + ca + ab} = \frac{b + a}{c + b}\]

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


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 two geometric means between the numbers 1 and 64 are 


Which term of the G.P. 5, 25, 125, 625, … is 510?


If p, q, r, s are in G.P. show that p + q, q + r, r + s are also in G.P.


A ball is dropped from a height of 80 ft. The ball is such that it rebounds `(3/4)^"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?


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 a G.P. if S5 = 1023 , r = 4, Find a


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


Select the correct answer from the given alternative.

The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is –


Select the correct answer from the given alternative.

If common ratio of the G.P is 5, 5th term is 1875, the first term is -


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:

Find the sum of the first 5 terms of the G.P. whose first term is 1 and common ratio is `2/3`


Answer the following:

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


Answer the following:

Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...


Answer the following:

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


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


The third term of a G.P. is 4, the product of the first five terms is ______.


The sum of infinite number of terms of a decreasing G.P. is 4 and the sum of the terms to m squares of its terms to infinity is `16/3`, then the G.P. is ______.


If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n 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 ______.


If the expansion in powers of x of the function `1/((1 - ax)(1 - bx))` is a0 + a1x + a2x2 + a3x3 ....... then an is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×