## mathmath333 one year ago Iterative Series Question.

1. mathmath333

\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}}

2. perl

Pick $$\large X_o=1$$ , that seems easiest.

3. mathmath333

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

4. mathmath333

ohk thnks it looks option d is the correct one.

5. perl

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

6. perl

I agree

7. zzr0ck3r

Do you mean series or sequence?

8. zzr0ck3r

do you mean partial sum or term?

9. zzr0ck3r

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

10. perl

@zzr0ck3r How about the nth term of the series?

11. perl

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.

12. zzr0ck3r

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.

13. perl

I don't think she meant partial sum

14. zzr0ck3r

right I think I should have read first :)

15. perl

agreed, it was ambiguous :)