Sequences and series, the nth term, summation notation and its rules, arithmetic progressions, the sum of an arithmetic series and problems in context.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
Save $50, then $70, then $90 … How much after two years? An arithmetic series answers in one line — and shows why such savings grow without limit.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Copy these into your notebook in your own words — that is how they stick.
{aₙ}: an ordered list; aₙ gives the nth term.
The sum of the terms of a sequence.
Σ kaᵣ = kΣaᵣ; Σ(aᵣ + bᵣ) = Σaᵣ + Σbᵣ; Σ_{1}^{n} k = nk.
Tₙ = a + (n − 1)d.
Sₙ = ½n[2a + (n − 1)d] = ½n(a + l).
Subtract to get (n − m)d, then find a.
Every AP series diverges (d ≠ 0 or a ≠ 0).
Savings, steps, seating: identify a, d and n carefully.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (27 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [14 marks]
The first three terms of an arithmetic progression are 5, 9 and 13.
(a) Find the common difference and the 15th term. [3]
(b) Find the sum of the first 15 terms. [3]
(c) The sum of the first n terms is 860. Show that 2n² + 3n − 860 = 0 and hence find n. [5]
(d) Evaluate Σ from r = 1 to 15 of (4r + 1). [3]
Question 2 [13 marks]
Mrs Lee saves $120 in January, $150 in February, $180 in March and so on, increasing by $30 each month.
(a) Show that she saves $450 in December of the same year. [3]
(b) Calculate her total savings for the year. [3]
(c) She continues in the same way. After how many months will her total savings first exceed $10 000? [5]
(d) Explain why the total saved can never reach a fixed limit. [2]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.