Practice Flashcards
Flip to reveal answersHow do you spot that a question needs the geometric SUM (Sₙ), not the nth term (uₙ)?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 11 Flashcards — Sum of n terms
Sign up free to track progress and get spaced-repetition review schedules.
Question
How do you spot that a question needs the geometric SUM (Sₙ), not the nth term (uₙ)?
Answer
Look for a TOTAL — 'sum of', 'altogether', 'total saved' over terms that multiply by a constant ⇒ Sₙ = u₁(rⁿ − 1)/(r − 1). A single value ('the 8th term', 'value after 8 years') ⇒ uₙ = u₁rⁿ⁻¹.
Question
Which form of the geometric sum should you use?
Answer
Either works. Use (rⁿ − 1)/(r − 1) when r > 1 and (1 − rⁿ)/(1 − r) when 0 < r < 1 to keep the numbers positive.
Question
What do you need to use the geometric sum formula?
Answer
u₁, r and n. If r isn't given, find it first from two terms.
Question
Find S₅ for 3 + 6 + 12 + … .
Answer
u₁ = 3, r = 2: S₅ = 3(2⁵ − 1)/(2 − 1) = 3 × 31 = 93.
Question
How do you find the smallest n with Sₙ past a target?
Answer
Set Sₙ > target and solve for n; on Paper 2 scan the GDC table of Sₙ and round up to the next whole number.
Question
Why does the geometric sum formula need r ≠ 1?
Answer
If r = 1 every term equals u₁, so the sum is just n × u₁ (and the formula would divide by zero).
Question
Find S₄ for u₁ = 6, r = ½.
Answer
S₄ = 6(1 − 0.5⁴)/(1 − 0.5) = 6(0.9375)/0.5 = 11.25.
Question
Sₙ = 2(3ⁿ − 1). Find u₁ and r.
Answer
Compare with u₁(rⁿ − 1)/(r − 1): r = 3 and u₁/(3 − 1) = 2 ⇒ u₁ = 4.
Question
On Paper 2, how do you sum a geometric series on the GDC?
Answer
Use sum(seq(u₁ r^(x−1), x, 1, n)) or read a table of Sₙ. Round n up for 'smallest n' questions.
Question
How do you show a geometric sum equals a given closed form like a(bⁿ − 1)?
Answer
Substitute u₁ and r into Sₙ = u₁(rⁿ − 1)/(r − 1) and simplify until it matches. E.g. u₁ = 4, r = 3 → 4(3ⁿ − 1)/2 = 2(3ⁿ − 1).
Question
How do you find the total distance a dropped ball travels over n bounces?
Answer
Distance = the first drop + 2 × (sum of the rebound heights). The drop counts once; every rebound is travelled up and down. Use the finite geometric sum Sₙ for the rebound heights.
Read the notes
Full study notes for Sum of n terms
Topic 1.3 hub
Geometric sequences & series
More from Topic 1.3
All flashcards in this topic
Math AA SL exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free