The 21st term of an AP whose first two terms are -3 and 4, is

Options

A. 17
B. 137
C. 143
D. -143

Explanation

To find the 21st term of the arithmetic progression (AP) whose first two terms are -3 and 4, we can follow these steps:

### Step 1: Identify the first term (a) and the second term (a₂)
The first term \( a \) is given as -3, and the second term \( a_2 \) is given as 4.

### Step 2: Calculate the common difference (d)
The common difference \( d \) can be calculated using the formula:
\[ d = a_2 - a \]
Substituting the values:
\[ d = 4 - (-3) = 4 + 3 = 7 \]

### Step 3: Use the formula for the nth term of an AP
The nth term of an AP can be calculated using the formula:
\[ a_n = a + (n - 1) \cdot d \]
where \( a_n \) is the nth term, \( a \) is the first term, \( n \) is the term number, and \( d \) is the common difference.

### Step 4: Calculate the 21st term (a₂₁)
To find the 21st term, we substitute \( n = 21 \):
\[ a_{21} = a + (21 - 1) \cdot d \]
Substituting the known values:
\[ a_{21} = -3 + (21 - 1) \cdot 7 \]
\[ = -3 + 20 \cdot 7 \]
\[ = -3 + 140 \]
\[ = 137 \]

### Final Answer
The 21st term of the AP is **137**.

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