What is the eight term of the sequence 1, 4 ,9 ,16 ,25, ?

Options

A. 8
B. 64
C. 128
D. 200

Answer

To find the 8th term of the sequence 1, 4, 9, 16, 25, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Pattern**:
The given sequence is: 1, 4, 9, 16, 25.
We can observe that these numbers are perfect squares:
- 1 = 1²
- 4 = 2²
- 9 = 3²
- 16 = 4²
- 25 = 5²

2. **Generalize the Pattern**:
From the observation, we can generalize that the nth term of the sequence can be expressed as:
\[ a_n = n^2 \]
where \( n \) is the position of the term in the sequence.

3. **Find the 8th Term**:
To find the 8th term, we substitute \( n = 8 \) into the formula:
\[ a_8 = 8^2 \]

4. **Calculate the Value**:
Now we calculate \( 8^2 \):
\[ 8^2 = 64 \]

5. **Conclusion**:
Therefore, the 8th term of the sequence is \( 64 \).

### Final Answer:
The 8th term of the sequence is **64**.

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