It's very simple,

the first term will be 4, then the second term would be, 7, then 10,
hence the last number less than 50 will be 49.

so,

4, 7, 10,.....49

Generally, apply Arithmetic progression,

Tn = a + (n-1)d

Tn = last term
a = first term
n = number of terms (we have to find this)
d= difference

49 = 4 + (n-1) 3
n = 16

I hope it make sense to you.

To solve this problem, we need to determine how many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3.

Step 1: Understanding the problem
We need to find the integers that satisfy the condition "remainder of 1 when divided by 3". In other words, we are looking for numbers that, when divided by 3, have a remainder of 1.

Step 2: Finding the pattern
To find the pattern, we can start by listing some numbers and their corresponding remainders when divided by 3:
- 0 divided by 3 gives a remainder of 0
- 1 divided by 3 gives a remainder of 1
- 2 divided by 3 gives a remainder of 2
- 3 divided by 3 gives a remainder of 0
- 4 divided by 3 gives a remainder of 1
- 5 divided by 3 gives a remainder of 2

From this pattern, we can observe that the remainders repeat in a cycle of length 3: 0, 1, 2, 0, 1, 2, and so on.

Step 3: Counting the numbers
To count the numbers that have a remainder of 1 when divided by 3, we can look at the pattern and identify the numbers in the sequence that have a remainder of 1:
- 1 (the first number in the sequence)
- 4 (the fourth number in the sequence)
- 7 (the seventh number in the sequence)
- 10 (the tenth number in the sequence)
- ...

We can see that the numbers that have a remainder of 1 when divided by 3 are in a sequence that starts at 1 and increases by 3 each time.

Step 4: Finding the count
To find the count of these numbers within the range of 0 to 50, inclusive, we need to determine the highest number in this sequence that is less than or equal to 50. We can do this by subtracting 1 from 50 and dividing the result by 3:
(50 - 1) / 3 = 49 / 3 = 16 remainder 1

Therefore, there are 16 numbers from 0 to 50, inclusive, that have a remainder of 1 when divided by 3.

Step 5: Final answer
The correct answer is option C) 17.