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A sequence is generated by the rule that the xth term is x⊃2 + 1 for each positive integer x. In this sequence, for any value x > 1, the value of (x + 1)th term less the value of xth term is —
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- 2x² + 1
- x² + 1
- 2x + 1
- x + 2
- 2x² + 1
Correct Option: C
Given in question , xth term = x⊃2 + 1
(x + 1)th term = (x + 1)⊃2 + 1
According to question,
(x + 1)th term – xth term = (x + 1)² + 1 – (x² + 1)
∴ Required answer = x² + 2x + 1 + 1 – x² – 1 = 2x + 1
