Write the first five terms of the sequences whose nth term is

Question:

Write the first five terms of the sequences whose nth term is  $a_{n}=(-1)^{n-1} 5^{n+1}$

Solution:

Substituting = 1, 2, 3, 4, 5, we obtain

$\mathrm{a}_{1}=(-1)^{1-1} 5^{1+1}=5^{2}=25$

$\mathrm{a}_{2}=(-1)^{2-1} 5^{2+1}=-5^{3}=-125$

$\mathrm{a}_{3}=(-1)^{3-1} 5^{3+1}=5^{+}=625$

$\mathrm{a}_{4}=(-1)^{4-1} 5^{4+1}=-5^{5}=-3125$

$\mathrm{a}^{5}=(-1)^{5-1} 5^{5+1}=5^{6}=15625$

Therefore, the required terms are 25, –125, 625, –3125, and 15625.