Answer :
To determine the next term of the sequence 1, 2, 4, 8, 16, .... using inductive reasoning, we first observe the pattern in the given sequence.
1. Identify the pattern:
- Start by writing down the sequence: [tex]\(1, 2, 4, 8, 16, ...\)[/tex].
- Notice the relationship between consecutive terms:
1. [tex]\(2 = 1 \times 2\)[/tex]
2. [tex]\(4 = 2 \times 2\)[/tex]
3. [tex]\(8 = 4 \times 2\)[/tex]
4. [tex]\(16 = 8 \times 2\)[/tex]
Each term is obtained by multiplying the previous term by 2.
2. Calculate the next term:
- Following the discovered pattern, the next term after 16 can be determined by multiplying 16 by 2:
[tex]\[ 16 \times 2 = 32 \][/tex]
3. Comparison with given options:
- The next term calculated (32) should be compared with the provided multiple-choice options:
- Option 64
- Option 256
- Option 128
- Option 32
4. Select the correct answer:
- Since 32 matches our calculated next term, 32 is the correct answer.
Thus, the next term in the sequence 1, 2, 4, 8, 16, ... is 32.
1. Identify the pattern:
- Start by writing down the sequence: [tex]\(1, 2, 4, 8, 16, ...\)[/tex].
- Notice the relationship between consecutive terms:
1. [tex]\(2 = 1 \times 2\)[/tex]
2. [tex]\(4 = 2 \times 2\)[/tex]
3. [tex]\(8 = 4 \times 2\)[/tex]
4. [tex]\(16 = 8 \times 2\)[/tex]
Each term is obtained by multiplying the previous term by 2.
2. Calculate the next term:
- Following the discovered pattern, the next term after 16 can be determined by multiplying 16 by 2:
[tex]\[ 16 \times 2 = 32 \][/tex]
3. Comparison with given options:
- The next term calculated (32) should be compared with the provided multiple-choice options:
- Option 64
- Option 256
- Option 128
- Option 32
4. Select the correct answer:
- Since 32 matches our calculated next term, 32 is the correct answer.
Thus, the next term in the sequence 1, 2, 4, 8, 16, ... is 32.
