$a_{n} = (- 1)^{n - 1} 5^{n + 1}$

Question

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Answer 1

Given, $a_{n} = (- 1)^{n - 1} . 5^{n + 1}$
Substituting $n = 1, 2, 3, 4, 5$ , we obtain
$a_{1} = (- 1)^{1 - 1} 5^{1 + 1} = 5^{2} = 25 a_{2} = (- 1)^{2 - 1} 5^{2 + 1} = - 5^{3} = - 125 a_{3} = (- 1)^{3 - 1} 5^{3 + 1} = 5^{4} = 625 a_{4} = (- 1)^{4 - 1} 5^{4 + 1} = 5^{5} = - 3125 a_{5} = (- 1)^{5 - 1} 5^{5 + 1} = 5^{6} = 15625$

Answer 2

Given,

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