In an AP, (a_{4m}=156), (a_m=48), and (d=6). What is the value of (m)?

Correct answer: 6

In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \(a_{4m}-a_m=(4m-m)d=3m\times6\). Since \(156-48=108\), we get \(18m=108\), so \(m=6\). For instance, if \(m=7\), the difference would be \(18\times7=126\), not 108. Exam tip: When two AP terms are given, subtract them directly instead of first finding the first term.