# List the first five terms of the sequence. a_{n} = (-1)^{n - 1} /4^{n}.

**Solution:**

Given the f(n) = a_{n} = (-1)^{n - 1} /4^{n}.

Let us take n = 1, 2, 3, 4, 5

When n = 1 ⇒ f(1) = a_{1} = (-1)^{1 - 1} / 4^{1} = (-1)^{0} / 4 = 1/4 [ since any number power zero is 1]

When n = 2 ⇒ f(2) = a_{2} = (-1)^{2 - 1} / 4^{2} = -1/16

When n = 3 ⇒ f(3) = a_{3} = (-1)^{3 - 1} / 4^{3} = 1/64

When n = 4 ⇒ f(4) = a_{4} = (-1)^{4 - 1} / 4^{4} = -1/256

When n = 5 ⇒ f(5) = a_{5} = (-1)^{5 - 1} / 4^{5} = 1/1024

Since, even powers of -1 give ‘1’ and odd powers of -1 give ‘-1’.

Therefore, the first five terms of the sequence are 1/4, -1/16, 1/64, -1/256, 1/1024

## List the first five terms of the sequence. a_{n} = (-1)^{n - 1} /4^{n}.

**Summary:**

The first five terms of the sequence. a_{n} = (-1)^{n - 1} /4^{n} are 1/4, -1/16, 1/64, -1/256, 1/1024.

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