TMUA Practice Question — Worked Solution

P2·Sequences & Series·6.0CrackTMUA Original

recurrencefibonacci-typemust-be-truemulti-statement

A sequence

a_{1}, a_{2}, a_{3}, \dots

of real numbers satisfies

a_{n + 2} = a_{n + 1} + a_{n}

for every

n \geq 1

. The values of

a_{1}

and

a_{2}

are not specified and may be any real numbers.

a_{5} = 2 a_{1} + 3 a_{2}

a_{1}

and

a_{2}

are integers, then every term of the sequence is an integer.

III

The sequence is increasing (that is,

a_{n + 1} > a_{n}

for every

n \geq 1

Which of the above must be true?

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