Final answer:
The nᵗʰ term of the sequence 13, 213, 413, 613, 813 is determined by the formula T(n) = 2n + 11. Each term is derived by plugging the term number n into this formula.
Step-by-step explanation:
The student is asking for the nᵗʰ term of a sequence. Looking at the pattern, it appears each term increases by 200 from the previous term; however, this is not immediately obvious due to the first two digits being fixed and the last term increasing by increments of 2. To find this nᵗʰ term, we analyze the sequence and note that each term can be written as 2n + 11, where n represents the position in the sequence starting from 1. So the first term is 2(1) + 11 = 13, the second term is 2(2) + 11 = 15, and so on.
To generalize, the nᵗʰ term T(n) of the sequence can be expressed as T(n) = 2n + 11. When n = 1, T(1) = 13, and so on. Therefore, to find the nᵗʰ term for any given n, you would simply plug n into the formula and calculate the result.