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If (a_n=kn+5) and (a_{15}-a_6=63), what is (a_{20})?

Answer and explanation

Correct answer: 145

Given \(a_n=kn+5\), we have \(a_{15}=15k+5\) and \(a_6=6k+5\). Thus, \(a_{15}-a_6=(15k+5)-(6k+5)=9k=63\), so \(k=7\). Therefore, \(a_{20}=20k+5=20\times7+5=145\). Hence, 145 is the correct option. Choosing 140 would incorrectly omit the constant term \(+5\). Exam tip: when subtracting two terms, the same constant term cancels out.

Related tags

Arithmetic ProgressionNth TermAlgebraic SubstitutionClass 10 MathematicsSequence FormulaFinding The $N$Th Term Of An ApFinding The N Th Term Of An ApArithmetic Progressions (Ap)

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