What you’ll learn
Model geometric sequences.
Key idea
At the first index no multiplication update has occurred, so the exponent must be zero.
Exponent n applies an extra update; check the first term and every ratio exactly.
Worked example
Enter the exact value or ordered values in the format requested below.
An abstract sequence starts at a1=-8 and each next term multiplies the previous by 3; n is a positive integer. Write its explicit a_n rule.
- Term one is -8; every update multiplies the previous term by exact ratio 3.
- Term n follows n-1 multiplications; a_n=-8(3)^(n-1) gives -8, -24, -72, -216.
Answer: a_n=-8(3)^(n-1)
Quick Check
Choose which candidate representation satisfies the requirements of 'Model geometric sequences' and justify the choice.
An abstract sequence starts at a1=-4 and each next term multiplies the previous by 4; n is a positive integer. Table a1..a4: -4, -16, -64, -256. Select with ratio and start evidence.