### Video Transcript

Is the sequence π sub π equals
negative one to the power of π over 11π minus 22 increasing, decreasing, or
neither?

When weβre considering if a
sequence is increasing or decreasing, weβre comparing any term to the term before
it. If a sequence is increasing, then
any term π sub π must be greater than π sub π minus one. That must be true for all values of
π. Similarly, if a sequence is
decreasing, then any term of index π in a sequence must be less than the term
before it. What we can do is to work out the
first few terms of the sequence and see if the values are increasing, decreasing, or
neither.

So we could take the πth term, and
weβll start by substituting π is equal to one. So for the first term π sub one,
we have negative one to the power of one over 11 times one minus 22. When we simplify this, we get the
fraction negative 243 over 11. Now that weβve found the first
term, we can find the second term by substituting in π is equal to two. When we simplify negative one
squared over 11 times two minus 22, we get the fraction negative 483 over 22. We can find the third term in the
same way by substituting π is equal to three. This means that we get a third
term, π sub three, equal to negative 727 over 33.

We have at this point got three
terms in the sequence, but itβs a little difficult to see if theyβre increasing or
decreasing. So it might be helpful to find
their decimal equivalents. The first term is approximately
negative 22.09, the second term approximately negative 21.95, and the third term is
approximately negative 22.03. We notice that the second term is
greater than the first term. However, the third term is less
than the second term. That means that we canβt say that
for all values either π sub π is bigger than π sub π minus one or π sub π is
less than π sub π minus one. And that means that the sequence
isnβt increasing or decreasing, so it must be neither. The answer is that π sub π is
neither increasing nor decreasing.