Question

Iterative Series Question.

Answer 1

\(\large \color{black}{\begin{align}
&\normalsize \text{The nth element of the series is represented as:} \hspace{.33em}\\~\\
&X_{n}=(-2)^{n}X_{n-1} \hspace{.33em}\\~\\
&\normalsize \text{if} \ X_{0}=x\ \normalsize \text{and }\ x>0\ \hspace{.33em}\\~\\
&\normalsize \text{then the following is always true} \hspace{.33em}\\~\\
&(a.)\ X_{n} \ \normalsize \text{is positive if n is even} \hspace{.33em}\\~\\
&(b.)\ X_{n} \ \normalsize \text{is positive if n is odd} \hspace{.33em}\\~\\
&(c.)\ X_{n} \ \normalsize \text{is negative if n is even} \hspace{.33em}\\~\\
&(d.) \normalsize \text{None of these} \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

Pick \(\large X_o=1 \) , that seems easiest.

Answer 3

i think both option a and b are correct, what u think

Answer 4

ohk thnks it looks option d is the correct one.

Answer 5

The the first three values are
\[\Large{ X_o = 1 \\
\\X_1 = (-2)^1\cdot X_0= -2 \cdot 1 = -2
\\X_2 = (-2)^2\cdot X_1 = (-2)^2 \cdot (-2)= -8
\\X_3 = (-2)^3\cdot X_2 = (-8)(-8)=64
\\ X_4 = (-2)^4 \cdot X_3 = 16 \cdot 64 = 1024
}
\]

Answer 6

I agree

Answer 7

Do you mean series or sequence?

Answer 8

do you mean partial sum or term?

Answer 9

nth element of a series does not make sense...

Answer 10

@zzr0ck3r How about the nth term of the series?

Answer 11

for example
1 + 2 + 3 + 4 + ...
1 is the first term
2 is the second term
3 is the third term.
etc
It would just be easier to say the nth term of the sequence whose terms are come from a series.

Answer 12

yes for sure "term" makes sense, but as the question was phrased I was not sure if they were asking about the nth element in the sequence of partial sums of the series or just the nth element in the sequence.

Answer 13

I don't think she meant partial sum

Answer 14

right I think I should have read first :)

Answer 15

agreed, it was ambiguous :)