Sequences

A sequence u₁, u₂, u₃,... is defined by

where k is a positive constant.

Given that u₃ = –1

show that

Hence

find the value of k,

A sequence u₁, u₂, u₃... is defined by

Show that u₂ = 40

Find the value of u₃ and the value of u₄ Given that the sequence is periodic with order 4

write down the value of u₅

find the value of_r²⁵₁ u_r

A sequence of terms a₁, a₂, a₃, … is defined by

Show that this sequence is periodic.

State the order of this periodic sequence.

Find the value of

The sequence u₁, u₂, u₃, … is defined by

where k is an integer.

Given that u₁ + 2u₂ + u₃ = 0

show that

Find the value of k, giving a reason for your answer.

Find the value of u₃

The sequence u₁, u₂, u₃, … is defined by

where k is an integer. Given that u₁ + 2u₂ + u₃ = 0

show that

Find the value of k, giving a reason for your answer.

Find the value of u₃

A sequence of numbers a₁, a₂, a₃, … is defined by

where k is a constant. Given that ● the sequence is a periodic sequence of order 3 ● a₁ = 2

show that

For this sequence explain why k 1

Find the value of

A sequence u₁, u₂, u₃, … is defined by

A sequence U₁, U₂, U₃,... is defined by

Find the value of

Another sequence V₁, V₂, V₃,... is defined by

Find V₃ and V₄ in terms of k.

find the value of k.

A sequence a₁, a₂, a₃,… is defined by

Write down an expression for a₂ in terms of k.

find the value of k.

A sequence a₁, a₂, a₃,... is defined by

where k is a constant.

Find an expression for a₂ in terms of k.

find the two possible values of k.

A-sequence x,, x,,x,... is defined by

Find an expression for x, in terms of k. (1)

Hence find the value of ¥ x,

A sequence u₁, u₂, u₃,... satisfies

Given that u₂ = 9,

find the value of u₃ and the value of u₄,

A sequence of numbers a₁, a₂, a₃... is defined by

where c is a constant.

Write down an expression, in terms of c, for a₂

find the range of values of c.

A sequence of positive numbers is defined by

Find a₂ and a₃, leaving your answers in surd form.

A sequence a₁, a₂, a₃,... is defined by

where k is a constant.

Write down an expression for a₂ in terms of k.

find the value of k.

A sequence x₁, x₂, x₃, … is defined by

where a is a constant.

Find an expression for x₂ in terms of a.

Show that x₃ = a² – 3a – 3. Given that x₃ = 7,

find the possible values of a.

Sue is training for a marathon. Her training includes a run every Saturday starting with a run of 5 km on the first Saturday. Each Saturday she increases the length of her run from the previous Saturday by 2 km.

Show that on the 4th Saturday of training she runs 11 km.

Find an expression, in terms of n, for the length of her training run on the n th Saturday.

Show that the total distance she runs on Saturdays in n weeks of training is n (n + 4) km.

On the n th Saturday Sue runs 43 km.

Find the value of n.

Find the total distance, in km, Sue runs on Saturdays in n weeks of training.

A sequence is given by:

find the value of p,

write down the value of x₂₀₀₈.