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Solnce55 [7]
3 years ago
7

How many terms are in the arithmetic sequence 9, 2, −5, . . . , −187?

Mathematics
1 answer:
Fantom [35]3 years ago
4 0
9, 2, -5... so is going down by 7 each time, meaning the "common difference" is -7.

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=9\\
d=-7\\
a_n=-187
\end{cases}
\\\\\\
-187=9+(n-1)(-7)\implies -187=9-7n+7
\\\\\\
7n=9+7+187\implies 7n=203\implies n=\cfrac{203}{7}\implies \boxed{n=29}
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