Final answer:
The 37th term of the arithmetic sequence that starts with 262, 257, and 252 is found using the formula T(n) = a + (n-1)d. After calculating, the 37th term is determined to be 82 without the need for rounding.
Step-by-step explanation:
The student's question requires finding the 37th term of a sequence. Given the first three terms of the sequence are 262, 257, and 252, we can deduce that it is an arithmetic sequence with a common difference of -5 (as each term decreases by 5).
To find the 37th term, we'll use the formula for finding the nth term in an arithmetic sequence:
T(n) = a + (n-1)d
where T(n) is the nth term, a is the first term, n is the position of the term in the sequence, and d is the common difference. Plugging in our values gives us:
T(37) = 262 + (37-1)(-5)
Calculating the above expression:
T(37) = 262 - 180 = 82
Hence, the 37th term of the sequence is 82. There is no need for rounding since the sequence deals with integer numbers.