Friday

August 29, 2014

August 29, 2014

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

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 3:31pmLook 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.

**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...

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 - 1..The first 2 terms of a geometric progression are the same as the ...

math - The 3rd term in an arithmetic sequence is 12, the 7th term is 24, a) How...

maths - Choose the THREE options that define sequences that do not converge. ...