Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=(-1)^{n-1} 5^{n+1}$
Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=(-1)^{n-1} 5^{n+1}$
Substituting $n=1,2,3,4,5,$ we obtain
$a_{1}=(-1)^{1-1} 5^{1+1}=5^{2}=25$
$a_{2}=(-1)^{2-1} 5^{2+1}=-5^{3}=-125$
$a_{3}=(-1)^{3-1} 5^{3+1}=5^{4}=625$
$a_{4}=(-1)^{4-1} 5^{4+1}=-5^{5}=-3125$
$a^{5}=(-1)^{5-1} 5^{5+1}=5^{6}=15625$
Therefore, the required terms are $25,-125,625,-3125$ and $15625 .$
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