Find the 25th term of the progression 6+10+14+….

Explanation

To find the 25th term of the arithmetic progression (AP) given by the sequence 6, 10, 14, ..., we can follow these steps:

### Step 1: Identify the first term and common difference
The first term (a) of the sequence is:
- \( a = 6 \)

To find the common difference (d), we subtract the first term from the second term:
- \( d = 10 - 6 = 4 \)

### Step 2: Use the formula for the nth term of an AP
The formula for the nth term (Tn) 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 25th term, so we set \( n = 25 \):
\[ T_{25} = 6 + (25 - 1) \cdot 4 \]

### Step 4: Simplify the equation
Now, calculate \( 25 - 1 \):
- \( 25 - 1 = 24 \)

Now substitute this back into the equation:
\[ T_{25} = 6 + 24 \cdot 4 \]

### Step 5: Calculate \( 24 \cdot 4 \)
Now calculate \( 24 \cdot 4 \):
- \( 24 \cdot 4 = 96 \)

### Step 6: Add the results
Now add 6 to 96:
\[ T_{25} = 6 + 96 = 102 \]

### Conclusion
Thus, the 25th term of the arithmetic progression is:
\[ \boxed{102} \]

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