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.
