20. Special series-3
1. Find next numbers in the sequence `88511,16351,73155`
`88511`
`8+8=16`
`8-5=3`
`5xx1=5`
`1-:1=1`
`:.` Next number is `16351`
Similary `16351`
`1+6=7`
`6-3=3`
`3xx5=15`
`5-:1=5`
`:.` Next number is `73155`
Similary `73155`
`7+3=10`
`3-1=2`
`1xx5=5`
`5-:5=1`
`:.` Next number is `10251`
`:.` The next number for given series `88511,16351,73155` is `10251`
Solution-1
2. Find next numbers in the sequence `100,365,24,60`
100 years in a century.
365 days in a non-leap year.
24 hours in a day.
60 minutes in an hour.
60 seconds in a minute.
`:.` The next number for given series `100,365,24,60` is `60`
Solution-1
3. Find next 2 numbers in the sequence `365,12,7,24`
365 days in a year.
12 month in a year.
7 days in a week.
24 hours in a day.
60 minutes in an hour.
60 seconds in a minute.
`:.` The next 2 number for given series `365,12,7,24` are `60,60`
Solution-1
4. Find next numbers in the sequence `16,06,68,88,L8`
`16,06,68,88,L8`
We turn that upside-down
`87,88,89,90,91`
So previous possible numbers are
`86,87,88,89,90,91`
Then we turn it back right-side up again, and we have:
`16,06,68,88,L8,98`
Answer : `98`
`:.` The next number for given series `16,6,68,88,79` is `98`
Solution-1
5. Find next 3 numbers in the sequence `3917,3526`
`3917-391=3526`
So required number are
`3526-352=3174`
`3174-317=2857`
`2857-285=2572`
`:.` The next 3 number for given series `3917,3526` are `3174,2857,2572`
Solution-1
6. Find next 3 numbers in the sequence `8,18,11,15,5,4,14,9,19,1,17,6,16`
Spelling of numbers from 1 to 19, which is alphabetically written as
8 : eight
18 : eighteen
11 : eleven
15 : fifteen
5 : five
4 : four
14 : fourteen
9 : nine
19 : nineteen
1 : one
7 : seven
17 : seventeen
6 : six
16 : sixteen
So required number are
10 : ten
13 : thirteen
3 : three
Answer : `10,13,3`
`:.` The next 3 number for given series `8,18,11,15,5,4,14,9,19,1,17,6,16` are `10,13,3`
Solution-1
7. 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
8. Find next 3 numbers in the sequence `4,16,37,58,89,145`
Each number of the series is the sum of the squares of the individual digits contained
in the preceding number
`4^2=16`
`1^2+6^2=37`
`3^2+7^2=58`
`5^2+8^2=89`
`8^2+9^2=145`
So required number are
`1^2+4^2+5^2=42`
`4^2+2^2=20`
`2^2+0^2=4`
Answer : `42,20,4`
`:.` The next 3 number for given series `4,16,37,58,89,145` are `42,20,4`
Solution-1
9. Find next 2 numbers in the sequence `992,733,845,632`
middle digit is sum of digits of the product of other two digits
`9xx2=18,1+8=9` (middle digit in 992)
`7xx3=21,2+1=3` (middle digit in 733)
`8xx5=40,4+0=4` (middle digit in 845)
`6xx2=12,1+2=3` (middle digit in 632)
Similary
`5xx3=15,1+5=6` (middle digit in 563)
`4xx5=20,2+0=2` (middle digit in 425)
`:.` The next 2 number for given series `992,733,845,632` are `563,425`
Solution-1
10. Find next numbers in the sequence `13579,23456,3579,4567,579`
First two number 13579 & 23456 are of 5 digit
difference of first two digit : `23-13=10`
difference of third digit : `5-4=1`
difference of fourth digit : `7-5=2`
difference of last digit : `9-6=3`
Similarly,
Second two number 3579 & 4567 are of 4 digit
difference of first two digit : `45-35=10`
difference of third digit : `7-6=1`
difference of last digit : `7-5=2`
Similarly,
Third two number 579 & X are of 3 digit
difference of first two digit must be 10 : `57+10=67`, So the first two digit are
67
difference of last digit must be 1 : `9-1=8`, So, the last digit is 8
So the last number is 678
Answer : `13579,23456,3579,4567,579,678`
`:.` The next number for given series `13579,23456,3579,4567,579` is `678`
Solution-1
11. Find next 3 numbers in the sequence `849,352,768,493,527`
Here each number is of 3 digits divided into 1st digit and next 2 digits
849 is 8 and 49, in which 8 is Last digit of `3^(rd)` number and 49 is start of
`4^(th)` number
352 is 3 and 52, in which 3 is Last digit of `4^(th)` number and 52 is start of
`5^(th)` number
768 is 7 and 68, in which 7 is Last digit of `5^(th)` number and 68 is start of
`6^(th)` number
493 is 4 and 93, in which 4 is Last digit of `6^(th)` number and 93 is start of
`7^(th)` number
527 is 5 and 27, in which 5 is Last digit of `7^(th)` number and 27 is start of
`8^(th)` number
684 is 6 and 84, in which 6 is Last digit of `8^(th)` number and 84 is start of
`9^(th)` number
Answer : `684,935,276`
`:.` The next 3 number for given series `849,352,768,493,527` are `684,935,276`
Solution-1
12. Find next 3 numbers in the sequence `31,28,31,30`
Days in the English name of Month
January has 31 days
February has 28 days
March has 31 days
April has 30 days
So required number are
May has 31 days
June has 30 days
July has 31 days
Answer : `31,30,31`
`:.` The next number for given series `31,28,31,30` are `31,30,31`
Solution-1
13. Find next 3 numbers in the sequence `92,87,63,36,78`
`92,87,63` now add a mirror. thus the number will be `36,78,29`
So we get `29` as answer
`:.` The next number for given series `92,87,63,36,78` is `29`
Solution-1
14. Find next 3 numbers in the sequence `7,21,8,72,9`
Answer : `7,21,8,72,9,243,10,810`
`:.` The next 3 number for given series `7,21,8,72,9` are `243,10,810`
Solution-1
This material is intended as a summary. Use your textbook for detail explanation.
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