T_2 = 6 frac1/2 and T_10= 8frac1/2 determine the formula for the nth term.

Answer 1

To find the formula for the nth term, we need to notice the pattern in the given terms T_2 and T_10.

T_2 = 6frac1/2
T_10 = 8frac1/2

We can first observe that there is a constant difference between the terms:
T_10 - T_2 = 8frac1/2 - 6frac1/2 = 2

Now, let's look at the fraction part. We can see that the fraction remains the same in both terms, which is frac1/2.

Since we have already established a constant difference of 2 between the terms, we can assume that the formula for the nth term will involve multiplying n by 2.

Therefore, the formula for the nth term is:
T_n = 2n + frac1/2