To find the next number in the arithmetic sequence [tex]\( 70, 54, 38 \)[/tex], we need to follow these steps:
1. Identify the sequence: The given sequence is [tex]\( 70, 54, 38 \)[/tex].
2. Determine the common difference:
- Subtract the second term from the first term: [tex]\( 54 - 70 = -16 \)[/tex].
- Validate this by subtracting the third term from the second term: [tex]\( 38 - 54 = -16 \)[/tex].
- Hence, the common difference [tex]\( d \)[/tex] is [tex]\(-16\)[/tex].
3. Calculate the next term:
- The next term in the sequence can be found by adding the common difference to the last term in the sequence.
- The last term given is 38, so the next term will be: [tex]\( 38 + (-16) = 38 - 16 = 22 \)[/tex].
Thus, the next number in the arithmetic sequence is
[tex]\[ 22 \][/tex].
So the correct answer is [tex]\[ 22 \][/tex].
