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Write the first five terms of the sequence whose $\boldsymbol{n}^{\text {th }}$ term is $a_n=(-1)^{n-1} 5^{n+1}$
Solution:
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Verified Answer
Putting $n=1,2,3,4,5$
$\begin{aligned}
&a_1=(-1)^0 \cdot 5^{1+1}=5^2=25 \\
&a_2=(-1)^1 \cdot 5^{2+1}=-5^3=-125 \\
&a_3=(-1)^2 \cdot 5^{3+1}=5^4=625 \\
&a_4=(-1)^3 \cdot 5^{4+1}=-5^5=-3125 \\
&a_5=(-1)^4 \cdot 5^{5+1}=5^6=15625
\end{aligned}$
$\begin{aligned}
&a_1=(-1)^0 \cdot 5^{1+1}=5^2=25 \\
&a_2=(-1)^1 \cdot 5^{2+1}=-5^3=-125 \\
&a_3=(-1)^2 \cdot 5^{3+1}=5^4=625 \\
&a_4=(-1)^3 \cdot 5^{4+1}=-5^5=-3125 \\
&a_5=(-1)^4 \cdot 5^{5+1}=5^6=15625
\end{aligned}$
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