English

For the following G.P.s, find Sn 0.7, 0.07, 0.007, .....

Advertisements
Advertisements

Question

For the following G.P.s, find Sn

0.7, 0.07, 0.007, .....

Sum
Advertisements

Solution

a = 0.7 = `7/10`, r = `0.07/0.7 = 1/10 < 1`

Sn = `("a"(1 - "r"^"n"))/(1 - "r")`, for r < 1

= `(7/10[1 - (1/10)^"n"])/(1 - 1/10)`

= `7/9 (1 - 1/10^"n")`

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Sequences and Series - Exercise 2.2 [Page 31]

APPEARS IN

RELATED QUESTIONS

Which term of the following sequence: 

`2, 2sqrt2, 4,.... is 128`


Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.


The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.


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


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


Find three numbers in G.P. whose sum is 65 and whose product is 3375.


Find the sum of the following geometric progression:

1, −1/2, 1/4, −1/8, ... to 9 terms;


Find the sum of the following series:

9 + 99 + 999 + ... to n terms;


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).


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.


A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.


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.


Express the recurring decimal 0.125125125 ... as a rational number.


Find k such that k + 9, k − 6 and 4 form three consecutive terms of a G.P.


If a, b, c are in G.P., prove that:

(a + 2b + 2c) (a − 2b + 2c) = a2 + 4c2.


If the first term of a G.P. a1a2a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is


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


The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 92. The common ratio of the original G.P. is 


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 255. If its common ratio is 2, then its first term is ______.


In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. 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 


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

2, 6, 18, 54, …


Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.


For the following G.P.s, find Sn

3, 6, 12, 24, ...


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


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


Find : `sum_("r" = 1)^oo (-1/3)^"r"`


Find : `sum_("n" = 1)^oo 0.4^"n"`


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 perimeters of all the squares


Select the correct answer from the given alternative.

The common ratio for the G.P. 0.12, 0.24, 0.48, is –


Select the correct answer from the given alternative.

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


Answer the following:

For a sequence Sn = 4(7n – 1) verify that the sequence is a G.P.


Answer the following:

If for a G.P. t3 = `1/3`, t6 = `1/81` find r


Answer the following:

Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`


If the pth and qth terms of a G.P. are q and p respectively, show that its (p + q)th term is `(q^p/p^q)^(1/(p - q))`


The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252cm2. The length of the longest edge is ______.


If `e^((cos^2x + cos^4x + cos^6x + ...∞)log_e2` satisfies the equation t2 – 9t + 8 = 0, then the value of `(2sinx)/(sinx + sqrt(3)cosx)(0 < x ,< π/2)` 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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×