If (a_n=2^n+n), what will be the first four terms?
Answer and explanation
Correct answer: (3,6,11,20)
Substitute \(n=1,2,3,4\) respectively: \(a_1=2^1+1=3\), \(a_2=2^2+2=6\), \(a_3=2^3+3=11\), and \(a_4=2^4+4=20\). Hence, the correct sequence is \((3,6,11,20)\). Option C has the correct first and fourth terms, but its second and third calculations are incorrect. Exam tip: evaluate \(2^n\) first, then add \(n\).
Frequently asked questions
What is the correct answer to this question?
(3,6,11,20)
Why is this the correct answer?
Substitute \(n=1,2,3,4\) respectively: \(a_1=2^1+1=3\), \(a_2=2^2+2=6\), \(a_3=2^3+3=11\), and \(a_4=2^4+4=20\). Hence, the correct sequence is \((3,6,11,20)\). Option C has the correct first and fourth terms, but its second and third calculations are incorrect. Exam tip: evaluate \(2^n\) first, then add \(n\).
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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