Final answer:
The nᵗʰ term of the sequence 13, 413, 813, 1213, 1613 is found using the arithmetic sequence formula Tₙ = 400n - 387.
Step-by-step explanation:
The student is asking to find the nᵗʰ term of the sequence 13, 413, 813, 1213, 1613. To determine the pattern, we can look at the difference between the terms.
Here, each term increases by 400, indicating this is an arithmetic sequence. The first term (a₁) is 13, and the common difference (d) is 400.
To find out how many feet you would swim if you did 28 lengths in a swimming pool that is 65 feet long, you need to multiply the length of the pool by the number of lengths you would swim. In this case, you would multiply 65 feet by 28 lengths.
65 feet x 28 lengths = 1820 feet
Therefore, if you did 28 lengths in a swimming pool that is 65 feet long, you would swim 1820 feet.
To find the nᵗʰ term of an arithmetic sequence, we use the formula Tₙ = a₁ + (n - 1) * d. Plugging the given values into the formula gives us the nᵗʰ term as Tₙ = 13 + (n - 1) * 400. Simplifying this, we get Tₙ = 13 + 400n - 400, which simplifies further to Tₙ = 400n - 387. Therefore, the nᵗʰ term of the sequence is 400n - 387.