Question

Complete the sequence:
30, 56, 90,___, 182, 240

• A. 145
• B. 132
• C. 110
• D. 160

Answer 1

The Correct Option is B

To solve the sequence problem, we need to identify the pattern or rule that connects the numbers. Let's analyze the differences between consecutive terms in the sequence:

• The sequence given is: 30, 56, 90, ___, 182, 240. 
• Find the differences between consecutive terms:

Term	Value	Difference
1st and 2nd	30 to 56	56 - 30 = 26
2nd and 3rd	56 to 90	90 - 56 = 34
3rd and 4th	90 to ___	?
4th and 5th	___ to 182	182 - ___ = ?
5th and 6th	182 to 240	240 - 182 = 58

• Clearly, the differences themselves form a sequence: 26, 34, ..., ?, 58.
• To predict the missing difference, let's check the differences of these differences:

Difference	Value	Difference of Differences
\(a_1 = 26\) and \(a_2 = 34\)	34 - 26	8
\(a_2 = 34\) and \(a_3 = ?\)	? - 34	8

• The difference between consecutive differences is constant at 8. Thus, we can predict: \(a_3 = 34 + 8 = 42\).
• Using this difference, calculate the missing number in the original sequence:
• From 90, add the difference 42 to find the missing term: 90 + 42 = 132.

Therefore, the missing term in the sequence is 132, making the sequence: 30, 56, 90, 132, 182, 240.

The correct answer is 132.