If 10 times of 10th term is equal to 20 times of 20th term of an A.P. Find its 30th term.

Answer

To solve the problem, we need to find the 30th term of an arithmetic progression (A.P.) given that 10 times the 10th term is equal to 20 times the 20th term.

### Step-by-Step Solution:

1. **Understanding the Terms of A.P.:**
The nth term of an A.P. can be expressed as:
\[ A_n = A + (n - 1)d \]
where \( A \) is the first term and \( d \) is the common difference.

2. **Expressing the 10th and 20th Terms:**
- The 10th term (\( A_{10} \)):
\[ A_{10} = A + (10 - 1)d = A + 9d \]
- The 20th term (\( A_{20} \)):
\[ A_{20} = A + (20 - 1)d = A + 19d \]

3. **Setting Up the Equation:**
According to the problem, we have:
\[ 10 \times A_{10} = 20 \times A_{20} \]
Substituting the expressions for \( A_{10} \) and \( A_{20} \):
\[ 10(A + 9d) = 20(A + 19d) \]

4. **Expanding Both Sides:**
- Left-hand side:
\[ 10A + 90d \]
- Right-hand side:
\[ 20A + 380d \]
Thus, we have:
\[ 10A + 90d = 20A + 380d \]

5. **Rearranging the Equation:**
Bringing all terms involving \( A \) and \( d \) to one side:
\[ 10A - 20A + 90d - 380d = 0 \]
Simplifying this gives:
\[ -10A - 290d = 0 \]
or
\[ 10A + 290d = 0 \]

6. **Finding the Relationship:**
Dividing the entire equation by 10:
\[ A + 29d = 0 \]
This implies:
\[ A = -29d \]

7. **Finding the 30th Term:**
The 30th term (\( A_{30} \)) can be expressed as:
\[ A_{30} = A + (30 - 1)d = A + 29d \]
Substituting \( A = -29d \):
\[ A_{30} = -29d + 29d = 0 \]

### Conclusion:
The 30th term of the A.P. is:
\[ \boxed{0} \]