What you’ll learn
Model arithmetic sequences.
Key idea
Count gaps from index one, not the index itself.
Term n is n-1 gaps from term one; signed terms do not change the index convention.
Worked example
Enter the exact value or ordered values in the format requested below.
An abstract sequence starts at a1=-9, and each next term is previous term plus (1), for positive integer n. Write an explicit a_n rule.
- Term one is -9 and each next term adds signed difference 1.
- Index n is n-1 updates beyond index one; rule a_n=-9+1(n-1) produces [-9, -8, -7, -6].
Answer: a_n=-9+1(n-1)
Quick Check
Choose which candidate representation satisfies the requirements of 'Model arithmetic sequences' and justify the choice.
An abstract sequence starts at a1=-6, and each next term is previous term plus (-5), for positive integer n. Table a1..a4 is [-6, -11, -16, -21]. Select with start/difference evidence.