Final answer:
The 69th term (a69) of the arithmetic sequence 10, 6, 2, -2, can be calculated using the formula an = a1 + (n - 1)d, where the first term (a1) is 10 and the common difference (d) is -4. Thus, a69 equals 10 + 68(-4), which simplifies to -262.
Step-by-step explanation:
To find the 69th term (a69) of an arithmetic sequence, we can use the formula an = a1 + (n - 1)d, where a1 is the first term, n is the term number, and d is the common difference between the terms. Looking at the sequence given, 10, 6, 2, -2, we can see that the common difference is -4 (because 6 - 10 = -4, 2 - 6 = -4, and so on). To find a69, we substitute the known values into the formula:
- a1 = 10 (first term)
- n = 69 (since we're looking for the 69th term)
- d = -4 (common difference)
Now, calculate a69:
a69 = 10 + (69 - 1)(-4)
a69 = 10 + 68(-4)
a69 = 10 - 272
a69 = -262
Therefore, the 69th term of the sequence is -262.