Directions (1 - 3): Complete the following series.
1. 2 4 12 4 240 ?
e) None of these
2. 2 5 9 19 37 ?
e) None of these
3. 4 -8 16 -32 64 ?
e) None of these
Directions (4 - 5): Find the wrong term in the following given series.
4. 2 9 28 65 126 216 344
5. 10 26 74 218 654 1946 5834
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.
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.
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:
-8*4 = -32
-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 × 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.
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