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1. A sequence is given: 2, 6, 12, 20 …………. Find the next term.

  • A. 30
  • B. 30
  • C. 30
  • D. 30

Answer: Option A

Explanation:

Step 1: Find the difference between consecutive terms 
The given sequence is 2, 6, 12, 20.
First difference:
6−2=46 minus 2 equals 4
6−2=4

Second difference:
12−6=612 minus 6 equals 6
12−6=6

Third difference:
20−12=820 minus 12 equals 8
20−12=8
 
Step 2: Identify the pattern of the differences 
The differences between the terms (4, 6, 8) are increasing by 2 each time. The next difference in this pattern will be
8+2=108 plus 2 equals 10
8+2=10
.
Step 3: Calculate the next term 
To find the next term in the original sequence, add the next difference (10) to the last term (20).
20+10=3020 plus 10 equals 30
20+10=30
Answer: 
The next term in the sequence is 30.

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