Posted by **albert** on Thursday, May 12, 2011 at 3:22pm.

A sequence is defined by

un = 2×(−0.5)n + 3 (n = 1,2,3, . . .).

Choose the option that best describes the long-term behaviour of the

sequence.

Options

A un becomes arbitrarily small (that is, un → 0 as n→∞).

B un becomes arbitrarily large and negative (that is, un →−∞

as n→∞).

C un approaches 3 as n→∞ (that is, un → 3 as n→∞).

D un is unbounded and alternates in sign.

E un becomes arbitrarily large and positive (that is, un→∞

as n→∞).

F un approaches 2 as n→∞ (that is, un → 2 as n→∞

- maths -
**MathMate**, Thursday, May 12, 2011 at 3:31pm
Look at the behaviour of the first term:

2*(-0.5)^n (check, this is not what you posted).

We can make the following observations.

As n increases, the sign alternates.

As n->∞ the term approaches zero.

Based on these observations, can you make a choice from the list of possible answers? In the worst case, you should be able to eliminate quite a few choices.

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