LearnFun Comics#46
The Count's Staircase
Stairs go up, but not too high! Or do they?
Starring Momo
Arithmetic progressions · Class 10
Arithmetic progressions · Class 10
The Count's Staircase: Arithmetic progressions comic
Numbered Steps Park. Momo plays on the stairs.
Momo: Five steps to the top. Easy peasy!
The Sum Goblin: Ah, the nth step. You'll need to climb more each day!
Momo: More steps? But how many? And which day? Oh no!
Steps add up
Steps change daily same.
Climb higher each time.
Arithmetic Progression!
Momo: So each day, the steps get higher? Just by the same number?
The Sum Goblin: Day 1: 3 steps. Day 2: 5 steps. Day 3: 7 steps! See the pattern?
Momo: Like climbing 2 steps each day. 3, 5, 7... see the pattern?
Day 1: 3 steps
Day 2: 5 steps
Day 3: 7 steps
Momo's trick
Day n means: a + (n-1)d
For day 50: a + 49d
It's like counting in steps!
Momo: To find day 50, use a + 49d. Easy peasy!
Your turn, hero!
The Sum Goblin♥♥♥
Day 1: 1 step. Day 2: 3 steps. How many steps on Day 10?
19. 1 + (10-1)×2 = 19.
The Sum Goblin: Day 50: 101 steps! Pay up, moocher!
10 steps daily. Day 50: how many steps?
500. 10 + (50-1)×10 = 500.
The final battle
The Sum Goblin♥♥♥
If Day 1 costs ₹10 and Day 50 costs ₹500, what is the daily increase in toll? answer: 9
10. (500-10)/49 = 10
The Sum Goblin: You can't add 100 steps! My plan is a joke!
Momo: Day 50: 101 steps. Not a joke, but a rule! 3 plus 2 times (50-1).
By noon, all 101 steps were paid. And the goblin was learning.
The End?
Villain card won! Answer again in a few days and it turns gold.
Remember
- Each day adds the same number.
- Use a + (n-1)d to find any day.
- It's like counting in steps!
But what's next? The goblin's note falls. 'Next problem: Fibonacci!'
A comic book about Arithmetic progressions. Follow Momo, learn the idea, and answer three questions to beat The Sum Goblin.