Step-by-step Solution:

Correct Answer: Option 3 : 40
Calculation:
Sequences:
17, 21, 25, ... 817
16, 21, 26, ... 851

Common difference of the first sequence:
\( d_1 = 21 - 17 = 4 \)

Common difference of the second sequence:
\( d_2 = 21 - 16 = 5 \)

Now, LCM of \( d_1 \) and \( d_2 \):
\( \text{LCM} = 4 \times 5 = 20 \)
So, the common difference: \( d = 20 \)

The first common term in both sequences is 21.
Hence, \( a = 21 \)

New sequence:
\( a, a + d, a + 2d, \dots \) or \( 21, 41, 61, 81, \dots 801 \)

As we know, the \( n \)-th term:
\( a + (n - 1) d = 801 \)
\( 21 + (n - 1) \times 20 = 801 \)
\( (n - 1) \times 20 = 780 \)
\( n - 1 = 39 \)
\( n = 40 \)

The total number of terms common in both the sequences is 40.