If (a_1=4) and (a_{n+1}=a_n+2n), what is (a_4)?
Answer and explanation
Correct answer: 16
Apply the recursive rule successively with n=1, 2, and 3: a_2=4+2(1)=6, a_3=6+2(2)=10, and a_4=10+2(3)=16. Therefore, the correct answer is 16. The value 14 would result from incorrectly using n=2 in the final step; to find a_4, the last step uses n=3. Exam tip: starting from a_1, apply the rule three times to obtain a_4.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Apply the recursive rule successively with n=1, 2, and 3: a_2=4+2(1)=6, a_3=6+2(2)=10, and a_4=10+2(3)=16. Therefore, the correct answer is 16. The value 14 would result from incorrectly using n=2 in the final step; to find a_4, the last step uses n=3. Exam tip: starting from a_1, apply the rule three times to obtain a_4.
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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