progression probs.......help

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atul duggal's picture
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let S be the sum of N terms of the following series s(n)=2^66-2^65-2^64.what is the sum of s(20)
a- 2^47
b- 2^12
c- 2^19
d none of these set

X is having 2000 elements in AP with the first term =1. what is the max number of elements set Y can have such that sun of no twi elements of Y is equal to 9 or a multiple of 9
a 890
b 891
.c 892
d none of these

in a sequence of terms a1,a2,a3,a4...the nth term ,a(n) for n >1,is given by a(n)=a(n-1)+a(n+1).if a7=6 and a14 =7find s26/s13 where si is the sum of all the terms from a1 to ai
a1/6
b -1/6
c 13/6
d cannot b determined

nishit's picture
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Answer to Q3
Given a (n) = a(n-1) + a(n+1)
=> a(n+1) = a(n) – a(n-1)
 
 Given a(7) = 6
 
a(7) = a(6) – a(5)
      = a(5) – a(4) – a(5)
        = - a(4)
        =  - a(3) + a(2)
        = -a(2) + a(1) + a(2)
        = a(1) =6
Numbers in the series repeat after 5 terms
 
Similarly a(14) = 7
 
a(14)  = a(13) – a(12)
          = a(12) – a(11) – a(12)
          = - a(11)
          = - a(10) + a (9)
          =  - a(9) + a(8) + a(9)
          =a(8) = 7
 
a(8) = a(7) – a (6)
=> a(6) = a(7) – a(8) = 6 – 7 = -1
 
a(7) = a(6) – a (5) => a(5) = -7
a(6) = a(5) – a(4) =>a(4) = -6
a(5) = a(4) – a(3) =>a(3) = 1
a(4) = a(3) – a(2) =>a(2) = 7
and a(1) = 6
a(0) = -1
 
So the series is 6, 7, 1, -6, -7, -1
6, 7, 1, -6, -7, -1
6, 7, 1, -6, -7, -1
 
Sum of first 26 terms = Sum of first 2 terms = 13
Sum of first 13 terms = 1 st term = 6
 
And the answer is 13/6

 ======================================= 

 Please check Q1 and Q2

Q1. Please confirm what the series is

 266  - 266  -264  - 263
or
 266  - 266  + 264  - 263
 
First series which you have written doesn’t make any sense.
 
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atul duggal's picture
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@nishit

hi

thanks for replying...both questions 1 and 2 are same as given in book....m also confused about the series...n 2nd question is same ..instead of twi its two

atul duggal's picture
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@nishit

hi

thanks for replying...both questions 1 and 2 are same as given in book....m also confused about the series...n 2nd question is same ..instead of twi its two....also if u can tell me how to find the last non zero last digit of 96!

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