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2015-06-06T16:25:28+08:00

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a_n=-18 \\\\ a_1\to 7 \\ a_2\to 2 \\\\ a_2=a_1+r \\\\ 2=7+r \\\\ 2-7=r \\\\ \boxed{r=-5} \\\\\\ a_n=a_1+(n-1)*r  \\\\ -18=7+(n-1)*(-5) \\\\ -18-7=(n-1)*(-5) \\\\ -25=(n-1)*(-5) \ \ \ |:(-5) \\\\ 5=n-1 \\\\ 5+1=n \\\\ \boxed{n=6} \Longrightarrow \boxed{\boxed{a_6=-18}}
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You can use every letter to define the common ratio, in my country,in Roumania, i was teach to use r for common ration in arithmetic sequence and q for geometric ones.
Oh ok sorry, it is just the standard variable for common difference here is d. The teacher might ask her that question so I am concerned.
No problem ;) I uderstand your worry but i would be here if the asker needs more details about my answer or if she doesn't understand something about it.
Ok. Sorry for questioning you.
No,you don't need to say sorry ;) it's ok ;)
2015-06-06T22:18:38+08:00

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Please note that:
a_2-a_1=a_3-a_2=a_4-a_3=...=a_n-a_{n-1}=d
a_2-a_1=2-7=-5=d

n= \frac{a_n-a_1}{d} +1= \frac{-18-7}{-5} +1= 6
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