Practice Flashcards
Flip to reveal answersYou are given u₁ = 7 and d = 4 and asked for the sum of the first 20 terms. What do you reach for — and what is the time-trap?
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
You are given u₁ = 7 and d = 4 and asked for the sum of the first 20 terms. What do you reach for — and what is the time-trap?
Answer
Go straight to Sₙ = (n/2)(2u₁ + (n − 1)d): S₂₀ = 10(14 + 19×4) = 900. Trap: do not waste time finding u₂₀ first — the u₁-and-d form needs only what you are given.
Question
A question asks 'how many terms until the running total first passes 500?'. How do you set it up?
Answer
It is a TOTAL, so use the sum: set Sₙ > 500 and solve for n, then round UP to the next whole number (on Paper 2, scan the GDC table of Sₙ). Spot 'total/altogether' ⇒ Sₙ, not uₙ.
Question
How do you choose which sum formula to use?
Answer
Know u₁ and d → use (n/2)(2u₁ + (n − 1)d). Know u₁ and the last term → use (n/2)(u₁ + uₙ).
Question
If you are told Sₙ as a formula, how do you find the first term?
Answer
u₁ = S₁ — substitute n = 1 into the sum. Example: Sₙ = 2n² + 3n ⇒ u₁ = 5.
Question
How do you recover any term from a sum formula Sₙ?
Answer
uₙ = Sₙ − Sₙ₋₁ — the running total up to n minus the running total up to n − 1.
Question
How can you tell a sequence is arithmetic from its sum?
Answer
Its sum is a quadratic in n with no constant term (Sₙ = an² + bn). The common difference is 2a.
Question
In an arithmetic sequence u₅ = 20 and S₅ = 70. How do you find u₁?
Answer
Use S₅ = (5/2)(u₁ + u₅): 70 = (5/2)(u₁ + 20) ⇒ u₁ + 20 = 28 ⇒ u₁ = 8.
Question
Why is there a factor of n/2 in the sum formula?
Answer
Pairing the first and last terms gives a constant total u₁ + uₙ, and there are n/2 such pairs, so Sₙ = (n/2)(u₁ + uₙ).
Question
How do you find d when given two sums, e.g. S₅ and S₆?
Answer
u₆ = S₆ − S₅ gives a term; combined with the sum formula you can solve for u₁ and d.
Question
Find S₈ for u₁ = 10, u₈ = 45.
Answer
S₈ = (8/2)(10 + 45) = 4 × 55 = 220.
Question
What is the difference between Sₙ and uₙ?
Answer
uₙ is a single term (the nth one); Sₙ is the total of the first n terms: Sₙ = u₁ + u₂ + … + uₙ.
Read the notes
Full study notes for Sum of n terms
Topic 1.2 hub
Arithmetic sequences & series
More from Topic 1.2
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