The Count's Staircase: Arithmetic progressions comic video

0:00 LearnFun Comics. The Count's Staircase. Stairs go up, but not too high! Or do they?

0:06 Numbered Steps Park. Momo plays on the stairs.

0:10 Five steps to the top. Easy peasy!

0:13 Ah, the nth step. You'll need to climb more each day!

0:17 More steps? But how many? And which day? Oh no!

0:21 Steps add up

0:23 Steps change daily same.. Climb higher each time.. Arithmetic Progression!

0:28 So each day, the steps get higher? Just by the same number?

0:32 Day 1: 3 steps. Day 2: 5 steps. Day 3: 7 steps! See the pattern?

0:39 Like climbing 2 steps each day. 3, 5, 7... see the pattern?

0:44 Day 1: 3 steps. Day 2: 5 steps. Day 3: 7 steps

0:49 Momo's trick

0:51 Day n means: a + (n-1)d. For day 50: a + 49d. It's like counting in steps!

0:59 To find day 50, use a + 49d. Easy peasy!

1:03 Your turn, hero! Day 1: 1 step. Day 2: 3 steps. How many steps on Day 10? A: 18. B: 19. C: 20. D: 21

1:19 The answer is 19. 1 + (10-1)×2 = 19.

1:25 Day 50: 101 steps! Pay up, moocher!

1:29 10 steps daily. Day 50: how many steps? A: 490. B: 500. C: 510. D: 520

1:43 The answer is 500. 10 + (50-1)×10 = 500.

1:49 The final battle If Day 1 costs ₹10 and Day 50 costs ₹500, what is the daily increase in toll? answer: 9 A: 8. B: 9. C: 10. D: 11

2:07 The answer is 10. (500-10)/49 = 10

2:12 You can't add 100 steps! My plan is a joke!

2:16 Day 50: 101 steps. Not a joke, but a rule! 3 plus 2 times (50-1).

2:22 By noon, all 101 steps were paid. And the goblin was learning.

2:28 Remember. Each day adds the same number. Use a + (n-1)d to find any day. It's like counting in steps!

2:36 But what's next? The goblin's note falls. 'Next problem: Fibonacci!'

2:41 Read this comic and answer the questions yourself, at learn fun dot in.