Final answer:
The 41st term of the arithmetic sequence is 385, which is found using the formula for the nth term of an arithmetic sequence, Tn = a + (n - 1)d, where the first term a=25 and the common difference d=9.
Step-by-step explanation:
The sequence provided (25, 34, 43) is an arithmetic sequence where each term increases by 9 from the previous term. To find the 41st term of this arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
Tn = a + (n - 1)d
where Tn is the nth term, a is the first term, n is the term number, and d is the common difference between terms.
For this sequence:
- a = 25 (the first term),
- d = 9 (the common difference),
- n = 41 (the term number we want to find).
Now we'll plug these values into the formula:
T41 = 25 + (41 - 1) × 9
T41 = 25 + 40 × 9
T41 = 25 + 360
T41 = 385
So, the 41st term of the sequence is 385.