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161. 3, 12,27,48, 75, 108,?

Discuss
Solution:
The terms of the given series are 3 x l2, 3 x 22, 3 x 32, 3 x 42, 3 x 52, 3 x 62,.....
So, missing term = 3 x 72 = 3 x 49 = 147.
162. 3, 7, 23, 95, ?

Discuss
Solution:
The pattern is x 2 + 1, x 3 + 2, x 4 + 3,.....
So, missing term = 95 x 5 + 4 = 479.
163. 6, 18, 3, 21, 7, 56, ?

Discuss
Solution:
Each term at an even place in the series is the product of its two adjacent terms.
Thus, if the missing term be x, then we have : 7 x x = 56 or x = 56 ÷ 7 = 8.
164. 4, 9, 25, ?, 121, 169, 289, 361

Discuss
Solution:
The given series consists of squares of consecutive prime numbers
i.e. 22, 32, 52,.....,
112, 132, 172, 192.
So, missing term = 72 = 49.
165. 6, 13,28,59,?

Discuss
Solution:
1st number : 62nd number : 6 X 2 +1 = 133rd number : 13 X 2 + 2 = 284th number : 28 X 2 + 3 = 59therefore5th number : 59 x 2 + 4 = 122
166. 4, 12, 36, 108, ?

Discuss
Solution:
The pattern is x 3.
So, missing term = 108 x 3 = 324.
167. Which term of the series 5, 8, 11, 14,.....is 320?

Discuss
Solution:
Clearly, 5 + 3 = 8, 8 + 3 = 11, 11 + 3 = 14, .....
So, the series is an A.P. in which a - 5 and d = 3.
Let 320 be the nth term of the series.
Then, 320 = 5 + (n - 1) x 3 or (n - 1) = 105 or n = 106.
168. 8, 9, 8, 7, 10, 9, 6, 11, 10, ?, 12

Discuss
Solution:
The given sequence is a combination of three series :
I. 1st, 4th, 7th, 10th terms i.e. 8, 7, 6, ?
II. 2nd, 5th, 8th, 11th terms i.e. 9, 10, 11, 12
III. 3rd, 6th, 9th terms i.e. 8, 9, 10 The pattern in I is - 1.
So, missing term = 6 - 1 = 5.
169. 3, 7, 15, ?, 63, 127

Discuss
Solution:
Each number in the series is one more than twice the preceding number.
So, missing term = (15 x 2) + 1 = 31.
170. 4, 10, ?, 82, 244, 730

Discuss
Solution:
Each number in the series is 2 less than thrice the preceding number.
So, missing number = (10 x 3) - 2 = 28.

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