Steady jar against doubling jar
"Steady jar against doubling jar" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Summing n terms of a GP" in Sequences and Series. Jar A puts in ₹100, then ₹50 more each week: an A.P. Jar B puts in ₹1, then doubles each week: a G.P. Slide the week and switch between each week's deposit and the running total. An A.P. adds the same amount each time; a G.P. with r > 1 multiplies by the same factor, and sooner or later it passes any A.P. Sₙ = a(rⁿ − 1)/(r − 1) gives the G.P. total at once. JEE Main asked 73 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Summing n terms of a GP in Sequences and Series. Change the values and watch what happens.
In JEE Main
42 shifts analysed
73 questions from Sequences and Series across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §8.4.2
- Write Sₙ = a + ar + … + arⁿ⁻¹ and multiply by r: rSₙ = ar + ar² + … + arⁿ. Subtracting, every middle term cancels and (1 − r)Sₙ = a − arⁿ.
- So for r ≠ 1, Sₙ = a(1 − rⁿ)/(1 − r) = a(rⁿ − 1)/(r − 1). The first form is handy when |r| < 1, the second when r > 1.
- If r = 1 every term equals a and Sₙ = na. The formula must not be used then, because it divides by zero.
- The ancestors over 10 generations number 2 + 4 + … + 1024 = 2(2¹⁰ − 1)/(2 − 1) = 2046.
- For 3 + 6 + 12 + … to 10 terms, S₁₀ = 3(2¹⁰ − 1) = 3069. For 1 + 1/2 + 1/4 + … to 6 terms, S₆ = (1 − (1/2)⁶)/(1 − 1/2) = 63/32.
- Working backwards: 3 + 6 + 12 + … reaches 765 when 3(2ⁿ − 1) = 765, so 2ⁿ = 256 and n = 8.
- An A.P. grows by the same amount each time; a G.P. with r > 1 grows by the same factor. Saving ₹100 in week 1 and ₹50 more each week gives a total of ₹4500 after 12 weeks; saving ₹1 in week 1 and doubling each week gives ₹4095 after 12 weeks but ₹8191 after 13, overtaking the ₹5200 of the steady plan.
Questions
3 answers
- What does the "Steady jar against doubling jar" simulation show?
- Jar A puts in ₹100, then ₹50 more each week: an A.P. Jar B puts in ₹1, then doubles each week: a G.P. Slide the week and switch between each week's deposit and the running total.
- Does JEE Main ask questions from Sequences and Series?
- Yes. JEE Main asked 73 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Summing n terms of a GP" in Sequences and Series (Class 11 Maths).
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