Final answer:
The formula for the nth number in the given sequence is a_n = a_n-1 - 16. The 10th number in the sequence is -70 and the 101st number is -166.
Step-by-step explanation:
The given sequence is 74, 58, 42, ...
To find the formula for the nth number, we need to look for a pattern in the sequence. By subtracting 16 from each number, we get the sequence: 58, 42, 26, ...
Now, we can see that each number in the new sequence is obtained by subtracting 16 from the previous number. So, the formula for the nth number is: an = an-1 - 16.
Using this formula, we can calculate the 10th number as follows:
- a1 = 74 (given)
- a2 = a1 - 16 = 58
- a3 = a2 - 16 = 42
- a4 = a3 - 16 = 26
- a5 = a4 - 16 = 10
- a6 = a5 - 16 = -6
- a7 = a6 - 16 = -22
- a8 = a7 - 16 = -38
- a9 = a8 - 16 = -54
- a10 = a9 - 16 = -70
So, the 10th number in the sequence is -70.
Similarly, we can calculate the 101st number by continuing the pattern:
- a10 = -70 (calculated)
- a11 = a10 - 16 = -86
- a12 = a11 - 16 = -102
- a13 = a12 - 16 = -118
- ...
- a100 = a99 - 16
- a101 = a100 - 16
Calculating each step, we find that the 101st number in the sequence is -166.