To determine which of the numbers given could be terms in the sequence [tex]\( a_n = 3n + 16 \)[/tex], we need to see if there exist integer values of [tex]\( n \)[/tex] that satisfy the equation [tex]\( a_n = 3n + 16 \)[/tex] for each given number.
### Checking [tex]\( 61 \)[/tex]:
1. Set up the equation: [tex]\( 3n + 16 = 61 \)[/tex]
2. Subtract 16 from both sides: [tex]\( 3n = 45 \)[/tex]
3. Divide by 3: [tex]\( n = 15 \)[/tex]
Since [tex]\( n = 15 \)[/tex] is an integer, 61 is a term in the sequence.
### Checking [tex]\( 48 \)[/tex]:
1. Set up the equation: [tex]\( 3n + 16 = 48 \)[/tex]
2. Subtract 16 from both sides: [tex]\( 3n = 32 \)[/tex]
3. Divide by 3: [tex]\( n = \frac{32}{3} = 10.\overline{6} \)[/tex]
Since [tex]\( n = 10.\overline{6} \)[/tex] is not an integer, 48 is not a term in the sequence.
### Checking [tex]\( 46 \)[/tex]:
1. Set up the equation: [tex]\( 3n + 16 = 46 \)[/tex]
2. Subtract 16 from both sides: [tex]\( 3n = 30 \)[/tex]
3. Divide by 3: [tex]\( n = 10 \)[/tex]
Since [tex]\( n = 10 \)[/tex] is an integer, 46 is a term in the sequence.
### Checking [tex]\( 64 \)[/tex]:
1. Set up the equation: [tex]\( 3n + 16 = 64 \)[/tex]
2. Subtract 16 from both sides: [tex]\( 3n = 48 \)[/tex]
3. Divide by 3: [tex]\( n = 16 \)[/tex]
Since [tex]\( n = 16 \)[/tex] is an integer, 64 is a term in the sequence.
Thus, the numbers that could be terms in the sequence [tex]\( a_n = 3n + 16 \)[/tex] are:
- [tex]\( 61 \)[/tex]
- [tex]\( 46 \)[/tex]
- [tex]\( 64 \)[/tex]
Therefore, the correct options are:
- A. 61
- C. 46
- D. 64
