###
**Directions (1 - 3):
Complete the following series.
**

**1. 2, 4, 12, 4, 240, ?**

a) 960

b) 1440

c) 1080

d) 1920

e) None of these

**2. 2, 5, 9, 19, 37, ?**

a) 76

b) 74

c) 75

d) 73

e) None of these

**3. 4, -8, 16, -32, 64,**

**?**

a) 128

b) -128

c) 192

d) -192

e) None of these

###
**Directions (4 - 5):
Find the wrong term in the following given series.
**

**4. 2, 9, 28, 65, 126, 216, 344**

a) 2

b) 28

c) 65

d) 126

e) 216

**5. 10, 26, 74, 218, 654, 1946, 5834**

a) 26

b) 74

c) 218

d) 654

e) 1946

### Answers:

**1. a)**2, 4, 12, 48, 240, ….

The pattern is: to arrive at a term, the previous term is being multiplied by (n+1) where ‘n’ keeps on increasing by 1 for every term.

**2**

**4**=

**2**× (2 + 0)

**12**=

**4**× (2 + 1)

**48**=

**12**× (2 + 2)

**240**=

**48**× (2 + 3)

⇒ Next term =

**240**× (**2**+ 4) = 240 × 6 =**1440**

**2. c)**2, 5, 9, 19, 37, …..

The pattern is: every number is arrived at previous number multiplied by 2 and then alternate addition and subtraction by 1 i.e.

**2**

**5=2×2+1**

**9=5×2-1**

**19=9×2+1**

**37=19×2-1**

the next term

**37**×2+1 =**75**

**3. b)**4, -8, 16, -32, 64, ….

The pattern is: Every number is arrived at by multiplying previous alternate number with ‘4’ as shown below:

**4*4 = 16**

**-8*4 = -32**

**16*4 = 64**

**-32*4 = -128**

Hence, ‘-128’ is the correct answer.

**4. e)**2, 9, 28, 65, 126, 216, 344.

The pattern in the series is that the series is triangular as shown below:

In the triangular series, the difference between consecutive terms is written below the numbers and then, difference between consecutive differences is
written below & this process carries on until all the difference become equal. In the figure above there was an error & we have corrected it.

**5. d)**10, 26, 74, 218, 654, 1946, 5834

The pattern is: to arrive at next term, the previous is multiplied by 3 and subtracted by 4:

**10**

**10**× 3 – 4 =

**26**

**26**× 3 – 4 =

**74**

**74**× 3 – 4 =

**218**

**218**× 3 – 4 =

**650**≠ 654

**650**× 3 – 4 =

**1946**

**1946**× 3 – 4 =

**5834**

Here, ‘654’ was wrong.

*Thanks.*

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