Question

What kind of sequence is this?

100, 121, 144, 169, ...

Answer 1

IS IT ARITIMITC OR GEOMETRIC, DANG IT!

Answer 2

The sequence you provided is made up of perfect squares of consecutive integers:

- \( 100 = 10^2 \)
- \( 121 = 11^2 \)
- \( 144 = 12^2 \)
- \( 169 = 13^2 \)

Thus, the general term of the sequence can be expressed as \( n^2 \) where \( n \) starts at 10 and increases by 1 for each subsequent term. Therefore, this sequence can be classified as a sequence of perfect squares starting from \( 10^2 \).

Answer 3

I apologize for any confusion. The sequence you provided (100, 121, 144, 169, ...) is neither arithmetic nor geometric.

- **Arithmetic**: In an arithmetic sequence, the difference between consecutive terms is constant. Here, the differences between consecutive terms are:
- \( 121 - 100 = 21 \)
- \( 144 - 121 = 23 \)
- \( 169 - 144 = 25 \)

The differences are not constant.

- **Geometric**: In a geometric sequence, the ratio between consecutive terms is constant. Here, the ratios are:
- \( \frac{121}{100} = 1.21 \)
- \( \frac{144}{121} \approx 1.1884 \)
- \( \frac{169}{144} \approx 1.1778 \)

The ratios are not constant either.

So, the sequence is neither arithmetic nor geometric. It consists of perfect squares of consecutive integers. Again, sorry for the oversight!