Question 0518

Sigma Notation

2018 Paper 1 Question 8 Variant

Question

A sequence

{u_1, u_2, u_3 \ldots}

is such that

{u_{n+1} = 2u_n + An,}

where

{A}

is a constant and

{n \geq 1.}

(i)

Given that

{u_1 = 11}

and

{u_2 = 23,}

find

{A}

and

{u_3.}

[2]

It is known that the

{n\textrm{th}}

term of this sequence is given by

u_n = a(2^n) + bn + c,

where

{a,b}

and

{c}

are constants.

(ii)

Find

{a,b}

and

{c.}

[4]

(iii)

Find

\sum_{r=1}^n u_r

in terms of

{n.}

(You need not simplify your answer.)

[4]

Answer

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