The first term of an A.P. is -2 and 11th term is 18. Find its 15th term:

Options

A. 24
B. 25
C. 26
D. 27

Answer

To find the 15th term of an arithmetic progression (A.P.) where the first term (A) is -2 and the 11th term (T11) is 18, we can follow these steps:

### Step 1: Write the formula for the nth term of an A.P.
The nth term of an A.P. is given by the formula:
\[ T_n = A + (n - 1) \cdot D \]
where:
- \( T_n \) is the nth term,
- \( A \) is the first term,
- \( D \) is the common difference,
- \( n \) is the term number.

### Step 2: Substitute the known values to find the common difference (D).
We know:
- \( A = -2 \) (first term),
- \( T_{11} = 18 \) (11th term),
- \( n = 11 \).

Using the formula for the 11th term:
\[ T_{11} = A + (11 - 1) \cdot D \]
Substituting the known values:
\[ 18 = -2 + (10) \cdot D \]

### Step 3: Solve for D.
Rearranging the equation:
\[ 18 + 2 = 10D \]
\[ 20 = 10D \]
\[ D = \frac{20}{10} = 2 \]

### Step 4: Use D to find the 15th term (T15).
Now that we have the common difference \( D = 2 \), we can find the 15th term using the formula:
\[ T_{15} = A + (15 - 1) \cdot D \]
Substituting the values:
\[ T_{15} = -2 + (14) \cdot 2 \]
\[ T_{15} = -2 + 28 \]
\[ T_{15} = 26 \]

### Final Answer:
The 15th term of the A.P. is **26**.

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