Final answer:
To find the 92nd term of the arithmetic sequence, we use the formula T_n = a + (n - 1)d. With a = 8 and d = 17, the 92nd term is calculated to be 1555.
Step-by-step explanation:
The student has asked for the 92nd term of an arithmetic sequence. The given sequence starts with 8, 25, 42, and so on. To find the 92nd term, we first need to determine the common difference (d) of the sequence. The difference between the second and first term is 25 - 8 = 17, and the difference between the third and second term is 42 - 25 = 17, confirming the common difference is 17.
Next, we use the arithmetic sequence formula for the nth term:
T_n = a + (n - 1)d
Where:
- T_n is the nth term we want to find,
- a is the first term of the sequence,
- n is the term number,
- d is the common difference.
Now we substitute the values:
T_92 = 8 + (92 - 1) × 17
T_92 = 8 + 91 × 17
T_92 = 8 + 1547
By solving this, we find that:
T_92 = 1555
Therefore, the 92nd term of the arithmetic sequence is 1555.