14. Special series-2
1. Find next 3 numbers in the sequence `1,10,11,100,101`
Binary number series
`1=1`
`2=10`
`3=11`
`4=100`
`5=101`
So required number are
`6=110`
`7=111`
`8=1000`
Answer : `1,10,11,100,101,110,111,1000`
`:.` The next 3 number for given series `1,10,11,100,101` are `110,111,1000`
Solution-1
2. Find next 3 numbers in the sequence `18,81,27,72,36`
First we consider only odd numbers : `18,27,36`
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18 |
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27 |
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36 |
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45 |
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54 |
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63 |
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`+`9 |
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`+`9 |
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`+`9 |
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`+`9 |
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`+`9 |
`:.` The next 3 number for given series `18,27,36` are `45,54,63`
Now, Second number is reverse number of first number
`18"'s reverse"=81`
`27"'s reverse"=72`
`36"'s reverse"=63`
So required number are
`45"'s reverse"=54`
`54"'s reverse"=45`
`63"'s reverse"=36`
Answer : `18,81,27,72,36,63,45,54,54,45,63,36`
`:.` The next 7 number for given series `18,81,27,72,36` are `63,45,54,54,45,63,36`
Solution-1
3. Find next 3 numbers in the sequence `1,6,120,5040,362880`
Numbers are Odd factorials
`1! =1`
`3! =6`
`5! =120`
`7! =5040`
`9! =362880`
So required number are
`11! =39916800`
`13! =6227020800`
`15! =1307674368000`
Answer : `39916800,6227020800,1307674368000`
`:.` The next 3 number for given series `1,6,120,5040,362880` are `39916800,6227020800,1307674368000`
Solution-1
4. Find next 3 numbers in the sequence `1,2,24,720`
Numbers are Even factorials
`0! =1`
`2! =2`
`4! =24`
`6! =720`
So required number are
`8! =40320`
`10! =3628800`
`12! =479001600`
Answer : `40320,3628800,479001600`
`:.` The next 3 number for given series `1,2,24,720` are `40320,3628800,479001600`
Solution-1
5. Find next 3 numbers in the sequence `3,1,4,1,5,9,2,6,5,3,5,8,9,7,9`
Numbers are decimal value of pi (`pi`)
Answer : `3.14159265358979323`
`:.` The next 3 number for given series `3,1,4,1,5,9,2,6,5,3,5,8,9,7,9` are `3,2,3`
Solution-1
6. Find next 3 numbers in the sequence `3,14,15,92`
Numbers are decimal value of pi (`pi`)
Answer : `3.141592653589`
`:.` The next 3 number for given series `3,14,15,92` are `65,35,89`
Solution-1
7. Find next 3 numbers in the sequence `15,20,20,6,6,19,19,5,14`
Converting numbers 1-26 to letters A-Z (means A is 1, Z is 26).
Sequence are the first letters of 'ONE' through 'TEN', then followed by the second
letters of 'ONE' through 'TEN'
15 = O, first letter of ONE
20 = T, first letter of TWO
20 = T, first letter of THREE
6 = F, first letter of FOUR
6 = F, first letter of FIVE
19 = S, first letter of SIX
19 = S, first letter of SEVEN
5 = E, first letter of EIGHT
14 = N, first letter of NINE
So required number are
20 = T, first letter of TEN
14 = N, second letter of ONE
23 = W, second letter of TWO
Answer : `20,14,23`
`:.` The next 3 number for given series `15,20,20,6,6,19,19,5,14` are `20,14,23`
Solution-1
8. Find next 3 numbers in the sequence `13,16,22,26,38,62`
`13+1xx3=13+3=16`
`16+1xx6=16+6=22`
`22+2xx2=22+4=26`
`26+2xx6=26+12=38`
`38+3xx8=38+24=62`
So required number are
`62+6xx2=62+12=74`
`74+7xx4=74+28=102`
`102+1xx0xx2=102+0=102`
Answer : `74,102,102`
`:.` The next 3 number for given series `13,16,22,26,38,62` are `74,102,102`
Solution-1
9. Find next 3 numbers in the sequence `4,8,16,13,7,14`
Here Second Number = SumOfDigits of first Number + MulOfDigits of first Number
`4=>(4)+(4)=4+4=8`
`8=>(8)+(8)=8+8=16`
`16=>(1+6)+(1xx6)=7+6=13`
`13=>(1+3)+(1xx3)=4+3=7`
`7=>(7)+(7)=7+7=14`
So required number are
`14=>(1+4)+(1xx4)=5+4=9`
`9=>(9)+(9)=9+9=18`
`18=>(1+8)+(1xx8)=9+8=17`
Answer : `9,18,17`
`:.` The next 3 number for given series `4,8,16,13,7,14` are `9,18,17`
Solution-1
10. Find next 3 numbers in the sequence `14,25,49,169,256`
Here Second Number = Square of SumOfDigits of first Number
`14=>(1+4)^2=5^2=25`
`25=>(2+5)^2=7^2=49`
`49=>(4+9)^2=13^2=169`
`169=>(1+6+9)^2=16^2=256`
So required number are
`256=>(2+5+6)^2=13^2=169`
`169=>(1+6+9)^2=16^2=256`
`256=>(2+5+6)^2=13^2=169`
Answer : `169,256,169`
`:.` The next 3 number for given series `14,25,49,169,256` are `169,256,169`
Solution-1
11. Find next 3 numbers in the sequence `1,2,3,6,4,5,12,60,5,6,7`
Consider 4 numbers group and every fourth number is the LCM of first three numbers
Lcm of `1,2,3=6`
Lcm of `4,5,12=60`
Lcm of `5,6,7=210`
`:.` The next number for given series `1,2,3,6,4,5,12,60,5,6,7` is `210`
Solution-1
This material is intended as a summary. Use your textbook for detail explanation.
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