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Explanation:

The first sequence can be written as 17, 17 + 4, 17 + 8, … , 417 and second sequence can be written as 16, 16 + 5, 16 + 10, … , 466

The common difference for the first sequence is 4 and that for the second sequence is 5 and both the sequences have 21 as the first common term.

∴ Common terms are 21, 21 + L, 21 + 2L, ...

[Here, L = LCM of 4 and 5 = 20]

∴ Common terms are 21, 21 + 20, 21 + 40, ...

The common terms have a common difference of 20 and first term as 21.

∴ Let Tn be the last common term, Tn = 21 + (n - 1) × 20

Now, Tn should be less than or equal to 417 

⇒ Tn = 21 + (n - 1) × 20 ≤ 417

⇒ 20n - 20 ≤ 396

⇒ n ≤ 416/20 = 20.8

Hence, the highest possible value of n is 20.

∴ The total number of terms which are common to both the sequences = 20

Hence, option (c).

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