Daniel J Smith Custom TMUA Set A Paper 2 · Question 12

A sequence $(a_n)$ is defined by $a_1=1$ and, for $n\geq1$ ,

a_{n+1}=\frac{a_n+4}{\sqrt{a_n+1}}

Which of the following statements is true?

(a_n)

is strictly decreasing for all

n

(a_n)

is bounded above but not bounded below

(a_n)

is bounded below by

1

and bounded above by

4

(a_n)

is bounded below by

2

and bounded above by

4

(a_n)

is bounded below by

1

but not bounded above

a_n>4

for all

n\geq2

GThe sequence

(a_n)

converges to

4

examday