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If (a_n=11n+c) and (a_5=72), what is (r) when (a_{5r}=512)?

Answer and explanation

Correct answer: \(9\)

Given \(a_n=11n+c\), use \(a_5=72\): \(72=11\times5+c\), so \(c=17\). Now \(a_{5r}=512\) gives \(512=11(5r)+17=55r+17\). Hence \(55r=495\), so \(r=9\). If \(r=10\), the term would be \(567\), not \(512\). Exam tip: first find the constant \(c\) from the given term, then substitute the required index in the formula.

Related tags

Arithmetic ProgressionNth TermAlgebraic SubstitutionAp IndexClass 10 MathematicsFinding The $N$Th Term Of An ApFinding The N Th Term Of An ApArithmetic Progressions (Ap)

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