Which option has (a=14) and (d=4)?

Correct answer: (14,18,22,26,\ldots)

The direct answer is option B: \((14,18,22,26,\ldots)\). In an arithmetic progression, \(a\) means the first term and \(d\) means the common difference. We need both conditions: first term must be 14, and each next term must increase by 4. Check option A: its first term is 4, although its difference is 4, so it fails the first condition. Check option B: the first term is 14, and \(18-14=4\), \(22-18=4\), and \(26-22=4\). Both conditions are satisfied, so B is correct. Check option C: its first term is 14, but its common difference is \(17-14=3\), not 4. Check option D: its difference is 4, but its first term is 18 rather than 14. Therefore only option B has \(a=14\) and \(d=4\). A useful formula is \(a_n=a+(n-1)d\), but no formula is needed here because the first two terms show the required values directly. The common mistake is checking only the difference or only the first term. Memory cue: for an AP option, inspect the first term for \(a\), then subtract consecutive terms for \(d\).