For an arithmetic progression with (a=8) and (a_6=43), what is (d)?
Answer and explanation
Correct answer: 7
The formula for an arithmetic progression is \(a_n=a+(n-1)d\). Substituting \(a_6=43\), \(a=8\), and \(n=6\) gives \(43=8+5d\). Thus, \(5d=35\), so \(d=7\). If 8 were chosen, the sixth term would be \(8+5\times8=48\), not 43. Exam tip: use \(n-1\), not \(n\), in the formula for \(a_n\).
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The formula for an arithmetic progression is \(a_n=a+(n-1)d\). Substituting \(a_6=43\), \(a=8\), and \(n=6\) gives \(43=8+5d\). Thus, \(5d=35\), so \(d=7\). If 8 were chosen, the sixth term would be \(8+5\times8=48\), not 43. Exam tip: use \(n-1\), not \(n\), in the formula for \(a_n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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