If (a_1=5) and (a_{n+1}=a_n+(2n-1)), what is (a_4)?
Answer and explanation
Correct answer: 14
Apply the recursive rule successively for n=1, 2, and 3. We get a_2=5+(2×1−1)=6, a_3=6+(2×2−1)=9, and a_4=9+(2×3−1)=14. Therefore, the correct answer is 14. The value 16 would result from incorrectly using n=4 for the next step, which is not needed here. Exam tip: To find a_4 from a_1, apply the rule three times.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Apply the recursive rule successively for n=1, 2, and 3. We get a_2=5+(2×1−1)=6, a_3=6+(2×2−1)=9, and a_4=9+(2×3−1)=14. Therefore, the correct answer is 14. The value 16 would result from incorrectly using n=4 for the next step, which is not needed here. Exam tip: To find a_4 from a_1, apply the rule three times.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Recursive rule.
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