Number series (add consecutive squares): find the next term. Sequence: 1, 5, 14, 30, 55, 91, ? Choose the correct next value.

Q: Number series (add consecutive squares): find the next term. Sequence: 1, 5, 14, 30, 55, 91, ? Choose the correct next value.

Given data 1, 5, 14, 30, 55, 91, ? Concept/Approach Examine first differences for a recognizable pattern. Step-by-step 5 − 1 = 4 = 2² 14 − 5 = 9 = 3² 30 − 14 = 16 = 4² 55 − 30 = 25 = 5² 91 − 55 = 36 = 6² Next difference = 7² = 49 ⇒ 91 + 49 = 140

Difficulty: Easy

130
140
150
160

Correct Answer: 140

Explanation:

Given data
1, 5, 14, 30, 55, 91, ?

Concept/Approach
Examine first differences for a recognizable pattern.

Step-by-step
5 − 1 = 4 = 2² 14 − 5 = 9 = 3² 30 − 14 = 16 = 4² 55 − 30 = 25 = 5² 91 − 55 = 36 = 6² Next difference = 7² = 49 ⇒ 91 + 49 = 140

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