NUMBER SEQUENCES PROBLEMS Try to guess the next number in each sequence using the simplest mathematical operations or ideas
1• 8723, 3872, 2387, ..........
2• 1, 4, 9, 18, 35, .............
3• 23, 45, 89, 177, .............
4• 7, 5, 8, 4, 9, 3, ..............
5• 3, 8, 15, 24, 35, .............
6• 2, 4, 5, 10, 12, 24, 27, .............
7• 1, 3, 4, 7, 11, 18, ..............
8• 99, 92, 86, 81, 77,..............
9• 0, 4, 2, 6, 4, 8, ..............
10• 1, 2, 6, 24, 120, ..............
11• 5, 7, 12, 19, 31, 50, ..................
12• 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107,...............
13• 126, 63, 190, 95, 286, 143, 430, 215, 646, 323, 970, ...............
14• 4, 7, 15, 29, 59, 117, ..............
15• 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9. 6 ...............
+130071 7• 1, 3, 4, 7, 11, 18, ..............This is the Lucas Series - L(n) - for n = 1,2,3,4........
This can also be generated by the Fibonacci Series where L(n) = Fib(n + 1) + Fib(n - 1) for n = ≥ 1
8• 99, 92, 86, 81, 77,.............. the next number is 74 .....
10• 1, 2, 6, 24, 120.............. = n!
11• 5, 7, 12, 19, 31, 50, .................. the next number is 81...... The pattern is L(n) + F(n+1) for n ≥ 2
14• 4, 7, 15, 29, 59, 117, ..............the next number is 235.......the pattern is twice the first number minus 1.....and then twice this result plus 1.....and this dual pattern repeats.....
+26396 1• 8723, 3872, 2387, ..........
$$8723, 3872, 2387, \textcolor[rgb]{1,0,0}{7238}$$
+26396 3• 23, 45, 89, 177, .............
$$23, 45, 89, 177, \textcolor[rgb]{1,0,0}{353} \qquad T_n = 2^{n-1}\cdot 22 +1 \quad n = 1,2, \cdots$$
+26396 4• 7, 5, 8, 4, 9, 3, ..............
$$\textcolor[rgb]{1,0,0}{7}, 5, \textcolor[rgb]{1,0,0}{8}, 4, \textcolor[rgb]{1,0,0}{9}, 3, \textcolor[rgb]{1,0,0}{10}$$
+26396 5• 3, 8, 15, 24, 35, .............
$$3, 8, 15, 24, 35, \textcolor[rgb]{1,0,0}{48} \qquad T_n = n\cdot(n+2) \quad n=1,2, \cdots$$
+130071 7• 1, 3, 4, 7, 11, 18, ..............This is the Lucas Series - L(n) - for n = 1,2,3,4........
This can also be generated by the Fibonacci Series where L(n) = Fib(n + 1) + Fib(n - 1) for n = ≥ 1
8• 99, 92, 86, 81, 77,.............. the next number is 74 .....
10• 1, 2, 6, 24, 120.............. = n!
11• 5, 7, 12, 19, 31, 50, .................. the next number is 81...... The pattern is L(n) + F(n+1) for n ≥ 2
14• 4, 7, 15, 29, 59, 117, ..............the next number is 235.......the pattern is twice the first number minus 1.....and then twice this result plus 1.....and this dual pattern repeats.....
