**Find the missing term in each of the following series**

Q1. 1, 6, 15, ?, 45, 66, 91 **[BBS, 2004]**

a. 25

b. 26

c. 27

d. 28

### Answer

**(d) 28**

Explanation:

The given sequence follows the pattern +5, +9, +13, +17, +21, ……

Thus 1 + 5 = 6, 6 + 9 = 15, ……

So, the missing term = 15 + 13 = 28

Q2. 2, 5, 9, 19, 37, ? **[CPO, 2003]**

a. 73

b. 75

c. 76

d. 78

### Answer

**(b) 75**

Explanation:

We have 2 x 2 + 1 = 5, 5 x 2 – 1 = 9, 9 x 2 + 1 = 19, 19 x 2 – 1 = 37, ….

So, missing term = 37 x 2 + 1 = 75

Q3. 4, 8, 28, 80, 244, ? **[BTM, 2006]**

a. 278

b. 428

c. 628

d. 728

### Answer

**(d) 728**

Explanation:

The terms of the given series are : 3^{1} + 1, 3^{2} – 1, 3^{3} + 1, 3^{4} – 1, ……..

So, missing term = 3^{6} – 1 = 729 – 1 = 728

Q4. 10000, 11000, 9900, 10890, 9801, ? **[PGDTM, 2006]**

a. 10241

b. 10423

c. 10781

d. 10929

### Answer

**(c) 10781**

Explanation:

Alternatively, we add and substract 10% of a term to obtain the next term of the series

Thus, 10000 + (10% of 10000) = 11000, 11000 – (10% of 11000] = 9900, 9900 + (10% of 9900) = 10890, 10890 – (10% of 10890) = 9801

So, missing term = 9801 + (10% of 9801) = 9801 + 980 = 10781

Q5. 0, 6, 24, 60, 120, 210, ?

a. 240

b. 290

c. 336

d. 504

### Answer

**(c) 336**

Explanation:

The given series is : 1^{3} – 1, 2^{3} – 2, 3^{3} – 3, 4^{3} – 4, ……..

So, Missing term = 7^{3} – 7 = 343 – 7 =336

Q6. 1, 4, 27, 16,, ?, 36, 343 [SNAP, 2004]

a. 25

b. 87

c. 120

d. 125

### Answer

**(d) 125**

Explanation:

The given series consists of cubes of odd numbers and squares of even numbers, i.e. 1^{3}, 2^{3}, 3^{3}, 4^{2}, ….

Missing term = 5^{3} = 125

Q7. 4, 6, 12, 14, 28, 30, ….

a. 32

b. 60

c. 62

d. 64

### Answer

**(b) 60**

Explanation:

The given sequence is a combination of two series:

I. 4, 12, 28, ? and II. 6, 14, 30, …..

Now, the pattern followed in each of the above two series is +8, +16, +32, ….

So, missing number = 28 + 32 = 60

Q8.1, 3, 6, 7, 9, ?, 12, 21

a. 10

b. 11

c. 12

d. 13

### Answer

**(d) 13**

Explanation:

The given sequence is a combination of two series

I. 1, 3, 7, ?, 21 and II. 3, 6, 9, 12

The pattern followed in I is +2, +4, … and the pattern followed in II is +3

So, missing number = 7 + 6 = 13

Q9. Which fraction comes next in the sequence 1/2, 3/4. 5/8, 7/16, ? **[MAT, 2005]**

a. 9/32

b. 10/17

c. 11/34

d. 12/35

### Answer

**(d) 13**

Explanation:

The numerators of the fractions in the given sequence form the series1,3, 5, 7, …. in which each term is obtained by adding 2 to the previous term

The denominators of the fractions form the series 2, 4, 8, 16 i.e. 2^{1}, 2^{2}, 2^{3}, 2^{4}

So, the numerator of the next fraction will be (7 + 2) = 9 and the denominator will be 2^{5}

= 32. So, The next term will be 9/32