30th term of the A.P. 10,7,4,….. Is

Options

A. 97
B. 77
C. `-77`
D. `-87`

Answer

To find the 30th term of the arithmetic progression (A.P.) given by the sequence 10, 7, 4, ..., we can use the formula for the nth term of an A.P.:

### Step-by-Step Solution:

1. **Identify the first term (A)**:
The first term of the A.P. is given as:
\[ A = 10 \]

2. **Calculate the common difference (D)**:
The common difference \(D\) can be calculated by subtracting the first term from the second term:
\[ D = \text{Second term} - \text{First term} = 7 - 10 = -3 \]

3. **Identify the term number (n)**:
We need to find the 30th term, so:
\[ n = 30 \]

4. **Use the formula for the nth term of an A.P.**:
The formula for the nth term \(A_n\) of an A.P. is given by:
\[ A_n = A + (n - 1) \times D \]
Substituting the values we have:
\[ A_{30} = 10 + (30 - 1) \times (-3) \]

5. **Calculate \(A_{30}\)**:
First, calculate \(n - 1\):
\[ n - 1 = 30 - 1 = 29 \]
Now substitute this back into the formula:
\[ A_{30} = 10 + 29 \times (-3) \]
Calculate \(29 \times (-3)\):
\[ 29 \times (-3) = -87 \]
Now substitute this value:
\[ A_{30} = 10 - 87 = -77 \]

6. **Final Result**:
Therefore, the 30th term of the A.P. is:
\[ A_{30} = -77 \]