Question 1

Find the sum of n terms of the given series. 1.2.4 +2.3.5 + 3.4.6 + ...

Accepted Answer

Put n = 1, now the sum of the series = 1.2.4 = 8 Put n = 1, in the options (a) 1(1 + 1) (1 + 2) = 6 (b) 1(1 + 1)/12 x (3 + 19 + 26) = 8 (c) (1 + 1) (1 + 2) (1 + 3)/4 = 6 (d) 1(1 + 1) (1 + 2) (1 + 3 )/3 = 8 As, the sum of series = 8 Hence, option (a) and (c) can be rejected. Now, put n = 2 Sum 1. 2. 4 + 2 . 3 . 5 = 38 Put n = 2, in option (b) 2(2 + 1)/12 (3 x 4 + 19 x 2 + 26)38 Hence, (b) is the correct option.

Question 2

In a geometric progression, the sum of the first and the last terms is 66 and the product of the second and the last second terms is 128. Determine the first term of the series?

Accepted Answer

Let a be the first term and and r be the common ratio of the GP. From the given problem, a + arn - 1 = 66 ...(i) Also, ar x arn - 2 = 128 ⇒ a2rn - 1 = 128 ... (ii) From Eq. (ii), a.arn - 1 = 128 arn - 1 = 128/ a On substitution this in Eq.(i), we get a + 128/a = 66 a2 - 66a + 128 = 0 a = [-b ± √b2 - 4ac] /2a = 66 ± √662 - 4 x 128 x 1)/2 = 64 or 2

Question 3

The 1st term of an HP is 1/17 and the product of the 2nd and 4th term equals to the products of 5th and 6th term of the HP. Find the 3rd term of the HP.?

Accepted Answer

The 1st term of an HP is 1/17 . Hence, for the corresponding AP, the terms is 17 . Here, a = 17 nth term of an AP is given by Tn = a + (n -1)d ∴ T2 = 17 + d, T4 = 17 + 3d T5 = 17 + 4d, T6 = 17 + 5d ∴ (17 + d) (17 + 3d) = (17 + 4d) (17 + 5d) ⇒ 289 + 51d + 17d + 3d2 = 289 + 85d + 68d + 20d2 ⇒ 68d + 3d2 = 153d + 20d2 ⇒ 17d2 = -85d ⇒ d = -5 ∴ 3rd term is T3 = a + 2d = 17 + 2(-5) = 17 - 10 = 7 Hence, for the corresponding HP, the 3rd term is 1/7.

Question 4

165, 195, 255, 285, .... 435

Accepted Answer

Series Pattern (15 x 11), (15 x 13), (15 x 17), (15 x 19), (15 x 23), (15 x 29) ∴ Missing term = (15 x 23) = 345

Question 5

2, 11, 38, 197, 1172, 8227, 65806

Accepted Answer

Series Pattern 2 x 3 + 5 = 11, 11 x 4 - 6 = 38 38 x 5 + 7 = 197, 197 x 6 - 8 = 1174 Should come in place of 1172 1174 x 7 + 9 = 8827 8827 x 8 - 10 = 65806 Clearly, 1172 is wrong and will be replaced by 1174.

Question 6

16, 19, 21, 30, 46, 71, 107

Accepted Answer

Series pattern 16 + 12 = 17 Should come in place of 19 17 + 22 = 21 ; 21+ 32 = 30; 30 + 42 = 46 ; 46 + 52 = 71 71 + 62 = 107 Clearly, 19 is wrong and will be replaced by 17.

Question 7

4, 2, 3.5, 7.5, 26.25, 118.125

Accepted Answer

Series pattern 4 x 0.5 = 2 2 x 1.5 = 3 Should come in place of 3.5 3 x 2.5 = 7.5 7.5 x 3.5 = 26.25 26.25 x 4.5 = 118.125 Clearly, 3.5 is wrong and is replaced by 3.

Question 8

20, 21, 25, 34, 50,?, 111

Accepted Answer

Series pattern 20 + 12 = 21, 21 + 22 = 25, 25 + 32 = 34, 34 + 42 = 50, 50 + 52 = 75 Should come in place of ' ? ' 75 + 62 = 111

Question 9

62, 87, 187, 412, 812,?

Accepted Answer

Series pattern 62 + 52 = 62 + 25 = 87 87 + 102 = 87 + 100 = 187 187 + 152 = 187 + 225 = 412 412 + 202 = 412 + 400 = 812 812 + 252 = 812 + 625 = 1437 Should come in place of '?'

Question 10

13, 35, 57, 79, 911,?

Accepted Answer

Series pattern The elements of the given series are the numbers formed by joining together consecutive add numbers in order i.e, 1 and 3, 3 and 5, 5 and 7, 7 and 9, 9 and 11,... ∴ Missing tern = Number formed by joining 11 and 13 = 1113

Question 11

What will come in place of question mark (?) in the following number series? 4, 3, 4, 7, 15, ?

Accepted Answer

4 3 4 7 15 ? ×1-1 ×1+1 ×2-1 ×2+1 ×3-1 15x3 - 1 = 45 - 1 = 44

Question 12

16, 33, 65, 131, 261, (....)

Accepted Answer

Each number is twice the preceding one with 1 added or subtracted alternatively. So, the next number is (2 x 261 + 1) = 523.

Question 13

Insert the missing number. 7, 26, 63, 124, 215, 342, (....)

Accepted Answer

Numbers are (23 - 1), (33 - 1), (43 - 1), (53 - 1), (63 - 1), (73 - 1) etc. So, the next number is (83 - 1) = (512 - 1) = 511.

Question 14

Find the odd man out. 41, 43, 47, 53, 61, 71, 73, 81

Accepted Answer

Each of the numbers except 81 is a prime number.

Question 15

Insert the missing number. 8, 7, 11, 12, 14, 17, 17, 22, (....)

Accepted Answer

There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22) increasing by 3 and 5 respectively.

Question 16

Find the odd man out? 396, 462, 572, 427, 671, 264.

Accepted Answer

Here the given series is 396, 462, 572, 427, 671, 264. In all the terms, the middle digit is the sum of first and third digit except 427. So the Odd number in the given series is 427.

Question 17

Find the odd man out. 2, 5, 10, 17, 26, 37, 50, 64

Accepted Answer

(1*1)+1 , (2*2)+1 , (3*3)+1 , (4*4)+1 , (5*5)+1 , (6*6)+1 , (7*7)+1 , (8*8)+1 But, 64 is out of pattern.

Question 18

Insert the missing number. 2, 4, 12, 48, 240, (....)

Accepted Answer

Go on multiplying the given numbers by 2, 3, 4, 5, 6. So, the correct next number is 1440.

Question 19

Insert the missing number. 3, 7, 6, 5, 9, 3, 12, 1, 15, (....)

Accepted Answer

There are two series, beginning respectively with 3 and 7. In one 3 is added and in another 2 is subtracted. The next number is 1 - 2 = -1.

Question 20

Find the odd man out. 6, 9, 15, 21, 24, 28, 30

Accepted Answer

Each of the numbers except 28, is a multiple of 3.

Odd Man Out and Series Questions