For what value of p, the following terms are three consecutive terms of an A.P. `4/5`, p,2.

Answer

To find the value of \( p \) such that \( \frac{4}{5}, p, 2 \) are three consecutive terms of an Arithmetic Progression (A.P.), we can use the property of A.P. that states the middle term is the average of the other two terms.

### Step-by-Step Solution:

1. **Identify the terms**: We have three terms in A.P.:
- First term \( a = \frac{4}{5} \)
- Second term \( b = p \)
- Third term \( c = 2 \)

2. **Use the A.P. property**: For three terms \( a, b, c \) to be in A.P., the following relationship must hold:
\[ b = \frac{a + c}{2} \]
Substituting the values of \( a \) and \( c \):
\[ p = \frac{\frac{4}{5} + 2}{2} \]

3. **Convert 2 to a fraction**: To add \( \frac{4}{5} \) and \( 2 \), we convert \( 2 \) into a fraction:
\[ 2 = \frac{10}{5} \]

4. **Add the fractions**: Now we can add the fractions:
\[ \frac{4}{5} + \frac{10}{5} = \frac{4 + 10}{5} = \frac{14}{5} \]

5. **Divide by 2**: Now, we need to divide \( \frac{14}{5} \) by \( 2 \):
\[ p = \frac{\frac{14}{5}}{2} = \frac{14}{5} \times \frac{1}{2} = \frac{14}{10} = \frac{7}{5} \]

6. **Conclusion**: Therefore, the value of \( p \) is:
\[ p = \frac{7}{5} \]

### Final Answer:
The value of \( p \) is \( \frac{7}{5} \).

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