Edexcel IAL P2 Sequences and Series Questions
Sequences by nth term and recurrence (increasing, decreasing, periodic); arithmetic and geometric series, sum to n terms, sum to infinity (|r| < 1), Σ notation.
- P2 · Pure Mathematics 2
- Calculator allowed
- 35 practice questions
What the questions test
The 35 P2 sequences and series practice questions cover:
Worked example 1
The second term of a geometric series is 12 and its sum to infinity is 64. Find the two possible values of the common ratio, $r$, and the corresponding values of the first term, $a$.
Mark scheme
- M1 for setting up the two equations: $ar = 12$ and $\frac{a}{1-r} = 64$.
- M1 for substituting $a = \frac{12}{r}$ to get $\frac{12/r}{1-r} = 64 \implies 12 = 64r(1-r)$.
- M1 for forming the quadratic $16r^2 - 16r + 3 = 0$.
- A1 for finding $r = 0.25$ and $r = 0.75$.
- A1 for finding the corresponding first terms: $a = 48$ and $a = 16$.
Worked example 2
The first, third, and seventh terms of an arithmetic sequence (with a non-zero common difference) form three consecutive terms of a geometric sequence. Show that the first term is twice the common difference ($a = 2d$).
Mark scheme
- M1 for writing the 1st, 3rd, and 7th terms as $a, a+2d, a+6d$.
- M1 for setting up the geometric ratio condition: $\frac{a+2d}{a} = \frac{a+6d}{a+2d}$.
- M1 for cross-multiplying and expanding: $(a+2d)^2 = a(a+6d) \implies a^2 + 4ad + 4d^2 = a^2 + 6ad$.
- M1 for rearranging to $4d^2 - 2ad = 0 \implies 2d(2d - a) = 0$.
- A1 for concluding that since $d \ne 0$, $2d - a = 0 \implies a = 2d$.
FAQ
What sequences and series is in Edexcel IAL P2?
Sequences by nth term and recurrence (increasing, decreasing, periodic); arithmetic and geometric series, sum to n terms, sum to infinity (|r| < 1), Σ notation.
Is P2 a calculator paper?
Yes, a calculator is allowed in P2, but method marks are only given for working you write down.
How are P2 sequences and series questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.