Sequence T1 is obtained by adding the corresponding terms of S(sub) and S(sub2). so that T(sub1) = {2.6, 3.39, 4.297, 5.3561, . . .}. We shall write T(sub1) = S(sub1) + S(sub2) to convey the addition of S(sub1) and S(sub2) in this way. Is T(sub1) an arithmetic or geometric sequence?

I am so confused. When I subtract the terms I get a common difference but it is not constant the whole time through (the terms will be different) And when I get the common ratio, I still get different answers. Am I interpreting this problem wrong?

Yes, You are.

Is T1 arithemetic or geo?

what is the difference between successive terms:
3.39-2.6=.79
4.297-3.39=.907
so it is not constant, so it is NOT arithemetic. Now, is it geometric
3.39/2.6 =1.2038...
4.297/3.39=1.267
the ratio is not constant ( assuming you typed the terms correctly) so it is not geometric.

To determine whether T(sub1) is an arithmetic or geometric sequence, let's analyze the given information.

First, let's consider the definitions of arithmetic and geometric sequences:

1. Arithmetic Sequence: In an arithmetic sequence, each term is obtained by adding a constant difference (d) to the previous term.

2. Geometric Sequence: In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio (r).

Now, let's break down the given sequence T(sub1) = {2.6, 3.39, 4.297, 5.3561, ...}.

To determine if T(sub1) is arithmetic:
- Subtract the terms.
- Check if the obtained differences are constant.

Let's calculate the differences between consecutive terms:

Difference between 2nd and 1st term: 3.39 - 2.6 = 0.79
Difference between 3rd and 2nd term: 4.297 - 3.39 ≈ 0.907
Difference between 4th and 3rd term: 5.3561 - 4.297 ≈ 1.0591

From the calculations, we can see that the differences are not constant. Therefore, T(sub1) is not an arithmetic sequence.

Now, let's check if T(sub1) is geometric:
- Divide the terms.
- Check if the obtained ratios are constant.

Let's calculate the ratios between consecutive terms:

Ratio between 2nd and 1st term: 3.39 / 2.6 ≈ 1.3038462
Ratio between 3rd and 2nd term: 4.297 / 3.39 ≈ 1.2678462
Ratio between 4th and 3rd term: 5.3561 / 4.297 ≈ 1.2452446

Again, the ratios are not constant. Therefore, T(sub1) is not a geometric sequence either.

Based on these calculations, T(sub1) does not fit the characteristics of either an arithmetic or geometric sequence. It may be a more complex sequence with a pattern that is not immediately apparent.