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101. 120, 99, 80, 63, 48, ?

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Solution:
The pattern is - 21, - 19, - 17, - 15,.....
So, missing term = 48 - 13 = 35.
102. 589654237, 89654237, 8965423, 965423, ?

Discuss
Solution:
The digits are removed one by one from the beginning and the end in order alternately
so as to obtain the subsequent terms of the series.
103. 3, 10, 101, ?

Discuss
Solution:
Each term in the series is obtained by adding 1 to the square of the preceding term.
So, missing term = (101)2 + 1 = 10202.
104. In the series 2, 6, 18, 54, ...... what will be the 8th term ?

Discuss
Solution:
Clearly, 2 x 3 = 6, 6 x 3 = 18, 18 x 3 = 54,.....
So, the series is a G.P. in which a = 2, r = 3.
Therefore 8th term = ar8-1 = ar7 = 2 x 37 = (2 x 2187) = 4374.
105. 125, 80, 45, 20, ?

Discuss
Solution:
The pattern is - 45, - 35, - 25, .....
So, missing term = 20 - 15 = 5.
106. 1, 1, 4, 8, 9, 27, 16, ?

Discuss
Solution:
The series consists of squares and cubes of consecutive natural numbers i.e. 12, 13, 22, 23, 32, 33, 42, .....
So, missing term = 43 = 64.
107. 1, 2, 3, 6, 9, 18, ?, 54

Discuss
Solution:
The pattern is x 2, x 3/2, x 2, x 3/2, x 2,.....
So, missing term = 18 x 3/2 = 27.
108. 6, 13, 25, 51, 101, ?

Discuss
Solution:
The pattern is x 2 + 1, x 2 - 1, x 2 + 1, x 2 - 1,.....
So, missing term = 101 x 2 + 1 = 203.
109. 5, 6, 9, 15, ?, 40

Discuss
Solution:
The pattern is + 1, + 3, + 6,....., i.e. + 1, + (1, + 2), + (1 + 2 + 3),.....
So, missing term = 15 + (1 + 2 + 3 + 4) = 25.
110. 1, 3, 4, 8, 15, 27, ?

Discuss
Solution:
The sum of any three consecutive terms of the series gives the next term.
So, missing number = 8 + 15 + 27 = 50.

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