What you’ll learn
Convert simple sequence descriptions.
Key idea
A recursive description needs both initial condition and previous-term update.
Recursive start and update are both required; a wrong recurrence may match one next term accidentally but not the continuation.
Worked example
Enter the exact value or ordered values in the format requested below.
Explicit arithmetic rule a_n=3+1(n-1) is defined for integer n≥1. Convert to start and recursive update: a1=...;a_n=... for n≥2.
- At n=1 the explicit rule a_n=3+1(n-1) gives first term 3.
- Each adjacent term changes by 1; recursive form a1=3;a_n=a_(n-1)+1, for n≥2. Term 5 is 7, after 4 updates.
Answer: a1=3;a_n=a_(n-1)+1
Quick Check
Evaluate a worked attempt at convert simple sequence descriptions, identify the first invalid step, and provide the correction.
Explicit arithmetic rule a_n=6-5(n-1) is defined for integer n≥1. Step 1 sets a1=6. Step 2 uses a_n=-5a_(n-1), replacing addition by multiplication. Find first invalid step and repair.