For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

Explanation

To find the value of \( n \) for which the \( n \)th terms of the two arithmetic progressions (APs) are equal, we will follow these steps:

### Step 1: Identify the first AP
The first AP is given as 63, 65, 67, ...
- First term \( a_1 = 63 \)
- Common difference \( d_1 = 65 - 63 = 2 \)

### Step 2: Write the formula for the \( n \)th term of the first AP
...