Recurrence Relations (AQA A-Level Mathematics): Quizzes

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Recurrence Relations
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What is a recurrence relation?

An equation defining a sequence from prior terms

Which method expands a recurrence relation step-by-step to find a pattern?

Substitution/Iteration

What do recurrence relations require to begin generating the sequence?

Initial terms

For an=c1an−1+c2an−2a_n = c_1a_{n-1} + c_2a_{n-2}, what is the characteristic equation?

x2−c1x−c2=0x^2 - c_1x - c_2 = 0

Given u0=7u_0 = 7 and un+1=5un−un2u_{n+1} = 5u_n - u_n^2, find u1u_1.

−14-14

For un=c+3n−2u_n = c + 3^{n-2} with u3=11u_3 = 11, find cc.

88

For un=8+3n−2u_n = 8 + 3^{n-2}, find u6u_6.

8989

What is the first step in solving non-homogeneous recurrence relations?

Solve the homogeneous part

What term describes a relation like an=c1an−1a_n = c_1a_{n-1}?

First-order

For un=3(un−1−k)u_n = 3(u_{n-1} - k) with u1=−4u_1 = -4 and u3=7u2+3u_3 = 7u_2 + 3, find kk.

−5-5

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