 Ram gets a box of chocolates, having 140 chocolates on his birthday. He ate 20 chocolates that day. He realized it was wrong and slowed down after that. He ate 6 chocolates every day after his birthday. Even 6 chocolates is a lot. How long did it take Ram to finish all the chocolates? Alright, so on the first day that is on his birthday, Ram had 140 chocolates and by the end of his birthday he ate 20 out of those. Meaning, the number of chocolates remaining by the end of his birthday would be 120 as he ate 20 out of 140. Now after his birthday, Ram slows down and eats 6 chocolates every day. So by the end of the second day, Ram would have 114 chocolates remaining in his box. Then he goes on and on the third day he eats 6 chocolates again. Meaning he has 108 chocolates left in his box now. So what we need to figure out is how many days it takes Ram to finish off all his chocolates. Meaning, by the end of which day would Ram have 0 chocolates in his box. So one of the most straightforward and direct ways to think about it is, we can keep on subtracting 6 chocolates every day till we get here. But imagine, if we had like 10,000 chocolates, would this way seem easier then? I don't think so. So let's think about some other way using which we can figure this thing out relatively easily. So the thing that stands out in these numbers over here is, that there is a pattern in the way Ram eats his chocolates. What I mean is, every other day Ram has 6 chocolates less than the previous day. So what we can say about this pattern is that every next term in this pattern is attained by subtracting 6 from the previous term. So whenever we have such a pattern that involves adding or subtracting a constant number to each term to get to the next term, we have an arithmetic progression. So the way Ram eats chocolates here is an arithmetic progression. So this means that the difference between any two consecutive terms is a constant number. And this constant number is known as the common difference of an AP. So negative 6 is the common difference over here. Now you can also observe that to get to our second term, we are adding this common difference once to the first term. Similarly to get to the third term, we are adding this common difference twice to the first term. And if we add the common difference thrice to the first term, we'll get our fourth term here. In other words, to get any n-th term in an AP, all we need to do is, we need to add the common difference n-1 times to the first term. So go ahead, pause this video and play with this for a while. Also, if you want to learn more, you can watch our previous videos. Also, try to figure out by the end of which day would Ram have zero chocolates in his box. So I hope you tried this on your own. Let's do this together now. So in this sequence, 120 is our first term. So this is a1. And what we need to find out is how many days it took Ram to finish all the chocolates. Meaning if it took Ram n days, if zero is the n-th term, we have to figure out how much is the value of this n. So zero is our n-th term, zero is n in this case. So let's put all these values in our equation over here and find out how many days it took Ram to finish off all the chocolates. So the n-th term is zero and this should be equal to the first term which is 120 plus n-1. n is the number of days that we need to figure out and the common difference is negative 6. So let's simplify this equation and find out n. And for doing that, the first thing I'll do is I'll subtract 120 from both sides. So over here, these two gets cancelled and I have 120 equal to n minus 1 times negative 6. So let me just create some space right over here. So as we need n, let's divide both sides of this equation by negative 6. So negative 6 times 20 is negative 120. So on the left-hand side, I have 20 and on the right-hand side, negative 6 times 1 is negative 6. So I have n minus 1 on the right-hand side. So on adding 1 on both sides of this equation, we'll get n equals to 21. So it takes 21 days for Ram to finish off all his chocolates. So Ram takes 21 days and is equal to 21 here.