Question

Identify the recursive formula for the following sequence:
mc002-1.jpg

an = an – 1 + 1 where a1 = 1

mc002-2.jpg

mc002-3.jpg

mc002-4.jpg

Answer 1

I can’t see the images you attached. Please type the sequence (the first few terms) or paste the four answer choices as text and I’ll pick the correct recursive formula.

While you paste, here’s how to find a recursive formula yourself:
- Write out the first several terms.
- Compute successive differences:
- If each term increases by the same amount d, it’s arithmetic: an = a_{n-1} + d with a1 given.
- If each term is multiplied by the same factor r, it’s geometric: an = r·a_{n-1} with a1 given.
- If terms follow a more complex relation (e.g. Fibonacci), you’ll need previous two terms: an = a_{n-1} + a_{n-2}, etc.
Examples:
- 1, 2, 3, 4, ... → an = a_{n-1} + 1, a1 = 1.
- 2, 5, 8, 11, ... → an = a_{n-1} + 3, a1 = 2.
- 3, 6, 12, 24, ... → an = 2·a_{n-1}, a1 = 3.
Paste the sequence or the choices and I’ll give the exact recursive formula.