# Let {an}n>= 1

## Homework Statement

If x is a real number, we de fine [x] as being the largest integer <= x. For example, [1.2] = 1,
[-1.1] = -2,  = 1, [11/3]3 = 3, . . .
Let {an}n>=1 be the numerical sequence de fined by:
a1 = 3; and an = a[n/2], for n>=2

(a) Give the terms a1; a2; ... ; a8 of this sequence.
(b) Prove that an = 3; For all n>=  1

## The Attempt at a Solution

I'm not sure what induction has to do with this... I don't really get it.

Mark44
Mentor

## Homework Statement

If x is a real number, we de fine [x] as being the largest integer <= x. For example, [1.2] = 1,
[-1.1] = -2,  = 1, [11/3]3 = 3, . . .
Let {an}n>=1 be the numerical sequence de fined by:
a1 = 3; and an = a[n/2], for n>=2

(a) Give the terms a1; a2; ... ; a8 of this sequence.
(b) Prove that an = 3; For all n>=  1

## The Attempt at a Solution

I'm not sure what induction has to do with this... I don't really get it.

Write out a few terms of the sequence to get a feel for what it's doing.
a1 = 3, a2 = ?, a3 = ?, a4 = ? And so on, through a8. That's part a.