The 71st term of 30,27, 24, 21, .... , is

Options

A. 5325
B. 240
C. 180
D. `-180`

Explanation

To find the 71st term of the sequence 30, 27, 24, 21, ..., we can follow these steps:

### Step 1: Identify the first term and the common difference
The first term \( a \) of the sequence is 30. To find the common difference \( d \), we can subtract the second term from the first term:
\[ d = 27 - 30 = -3 \]

### Step 2: Write the formula for the nth term of an arithmetic progression (AP)
The formula for the nth term \( a_n \) of an AP is given by:
\[ a_n = a + (n - 1) \cdot d \]

### Step 3: Substitute the values into the formula
We need to find the 71st term, so we substitute \( n = 71 \), \( a = 30 \), and \( d = -3 \) into the formula:
\[ a_{71} = 30 + (71 - 1) \cdot (-3) \]

### Step 4: Simplify the expression
Now, simplify the expression:
\[ a_{71} = 30 + 70 \cdot (-3) \]
\[ a_{71} = 30 - 210 \]
\[ a_{71} = -180 \]

### Conclusion
The 71st term of the sequence is \(-180\).

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