Find the 40th term of the progression 3,8,13,18,……

Options

A. 102
B. 198
C. 304
D. none of these

Answer

To find the 40th term of the progression 3, 8, 13, 18, we can follow these steps:

### Step 1: Identify the first term and the common difference
The first term (a) of the progression is 3.

To find the common difference (d), we subtract the first term from the second term:
\[ d = a_2 - a_1 = 8 - 3 = 5 \]

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

### Step 3: Substitute the values into the formula
We need to find the 40th term, so we set n = 40:
\[ T_{40} = 3 + (40 - 1) \cdot 5 \]

### Step 4: Simplify the expression
Now, calculate:
\[ T_{40} = 3 + 39 \cdot 5 \]
\[ T_{40} = 3 + 195 \]

### Step 5: Final calculation
Now, add the two numbers:
\[ T_{40} = 198 \]

Thus, the 40th term of the progression is:
\[ \boxed{198} \]

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