Write the first five terms of the sequences whose $n^{t h}$ term is :

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

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Solution

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

Putting n = 1, 2, 3, 4 and 5, we have

$a_{1} = (- 1)^{1 - 1} . 5^{1 + 1} = (- 1)^{\circ} . 5^{2} = 1 \times 25 = 25$

$a_{2} = (- 1)^{2 - 1} . 5^{2 + 1} = (- 1)^{1} . 5^{3} = - 1 \times 125 = - 125$

$a_{3} = (- 1)^{3 - 1} . 5^{3 + 1} = (- 1)^{2} . 5^{4} = - 1 \times 625 = 625$

$a_{4} = (- 1)^{4 - 1} . 5^{4 + 1} = (- 1)^{3} . 5^{5} = - 1 \times 3125 = - 3125$

$a_{5} = (- 1)^{5 - 1} . 5^{5 + 1} = (- 1)^{4} . 5^{6} = - 1 \times 15625 = 15625$

Thus, the first five terms are :

25, -125, 625, -3125 and 15625

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