If (a_n=3^n+2n), what will be the first three terms?
Answer and explanation
Correct answer: (5, 13, 33)
Given \(a_n=3^n+2n\): for \(n=1\), \(a_1=3^1+2(1)=5\); for \(n=2\), \(a_2=3^2+2(2)=13\); and for \(n=3\), \(a_3=3^3+2(3)=33\). Therefore, the first three terms are \((5, 13, 33)\). Option C has an incorrect second term because \(3^2+4=13\), not 14. Exam tip: evaluate and add both parts, \(3^n\) and \(2n\), for every value of \(n\).
Frequently asked questions
What is the correct answer to this question?
(5, 13, 33)
Why is this the correct answer?
Given \(a_n=3^n+2n\): for \(n=1\), \(a_1=3^1+2(1)=5\); for \(n=2\), \(a_2=3^2+2(2)=13\); and for \(n=3\), \(a_3=3^3+2(3)=33\). Therefore, the first three terms are \((5, 13, 33)\). Option C has an incorrect second term because \(3^2+4=13\), not 14. Exam tip: evaluate and add both parts, \(3^n\) and \(2n\), for every value of \(n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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