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Sequence and Series
by Sags ... - Wednesday, 17 June 2009, 05:10 PM
  Hi

Please post the solutions of the following:

17. Let the infinite series S1 = 1/12 + 1/32 + 1/52 +… and the infinite series

     S2 = 1/12 + 1/22 + 1/32 +… then,

    (a) S2 = 2S1                  (b) S2 = 3S1                      (c) S2 = 4 S1/3                (d)None of these


21. In a sequence, every term after the second term is twice the sum of the preceding two terms. If the ninth term of the sequence is 12 and the eleventh term is 30, find the thirteenth term of the sequence.


35. ‘Blackie’, the beetle, is sitting at the origin of the coordinate axis presently. He starts crawling in this manner- 1 unit to the right, 1/2 units up, 1/4 units right, 1/8 units down..continuing in this manner. At which point will ‘Blackie’ come to a stop?

     (a) (4/3, 2/5)                (b) (3/2, 4/3)           (c) (2/5, 4/3)                   (d)cannot be determined


39. For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the      previous two terms in that sequence. If the difference in squares of seventh and sixth terms of this      sequence is 517, what is the tenth term of this sequence?

     (a) 147                         (b) 76                              (c) cannot be determined     (d)None of these     


51. Find the sum:

Re: Sequence and Series
by userdce . - Wednesday, 17 June 2009, 06:31 PM
  17
(c) S2 = 4 S1/3  
Re: Sequence and Series
by nishant chawla - Wednesday, 17 June 2009, 11:03 PM
  21. 192
35. (a) (4/3, 2/5)
39. (d)None of these
51. please repost,question not visible
Re: Sequence and Series
by nishant chawla - Thursday, 18 June 2009, 08:26 AM
  i think for 39 we can't determine the 10th term
Re: Sequence and Series
by Sags ... - Monday, 22 June 2009, 04:28 PM
  hey guys
can u pls post solutions, as i have the answers, but i am in need of detailed solutions.

Thnks
Re: Sequence and Series
by Total Gadha - Tuesday, 23 June 2009, 02:34 AM
  Hi Sags,

Giving some hints:
1. S2 = 1/12 + 1/22 + 1/32 +… = 1/12 + 1/32 + 1/52... + 1/22 (1/12 + 1/22 + 1/32 +...) = S1 + S2/4

2. Given 9th and 11th term, find the 10th term and then proceed forward.

3. Make geometric series for horizontal and vertical movement.

4. F72 - F62 = 517 = 11 × 47 --> (F7 - F6)(F7 + F6) =
11 × 47. Find F6 and F7 and proceed.

Total Gadha
Re: Sequence and Series
by nishant chawla - Tuesday, 23 June 2009, 08:55 PM
  Hello TG sir

I have a doubt in q4


The product can be written in following ways

F7^2 - F6^2 = 517 = 11 × 47 --> (F7 - F6)(F7 + F6) = 11 × 47.
=517 x 1
=-517 x -1
= -11 x -47


F7 & F6 can have more than one value

=>F10 have more than one value
So, the ans should be can't be determined
Re: Sequence and Series
by poonam thakur - Thursday, 3 September 2009, 09:20 PM
  21.  Ans 192
Explanation:
Let the 8th term = x
9th term = 12
10th term = 24 + 2x
11th term = 72 + 4x = 30 (Hence x = -21/2)
12th term = 192 + 12x
13th term = 528 + 32x = 192

Thanks
Re: Sequence and Series
by Total Gadha - Friday, 4 September 2009, 02:57 AM
  Hi Nishant,

Fibonacci series involves only natural numbers.

Total Gadha
Re: Sequence and Series
by chetan chawla - Saturday, 16 May 2015, 10:52 AM
  ohow to solve third problem : black beetle moving horizontally and verticaly