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.

## Answer This Question

## Related Questions

- maths - A sequence is defined by un = 2×(−0.5)n + 3 (n = 1,2,3, . . .). ...
- algebra - can you check my answers please? What are the first three terms of the...
- algebra - the seventh term of a arithmetic sequence is 72 and the tenth term of ...
- math - 51.A sequence t is defined where the first term is –4. Each successive ...
- maths - fixed points - Fixed points of f? f(x) = 1/4x^2 - 1/8x - 5/8 a) use ...
- Math - Alpha writes the infinite arithmetic sequence 10, 8, 6, 4, 2, 0... Beta ...
- Math - A sequence is formed by adding together the corresponding terms of a ...
- maths - The method for completing the square can be used to write the expression...
- maths - given 1,0.5,4,o.25,7,0.125,10 assume this pattern continues consistently...
- Algebra - True or False 1. – 5, – 5, – 5, – 5, – 5, … is an arithmetic sequence...

More Related Questions