Question

Find an explicit formula for the geometric sequence −8,−40,−200,−1000...

Answer 1

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Answer 2

$a_n = (-8) \times 5^{n-1}$ is the explicit formula for the geometric sequence −8,−40,−200,−1000...

Solution:

The nth term of geometric sequence is given as:

$a_n = a_1 \times r^{n-1}$

Where,

n is the term location

$a_1$ is the first term of sequence

r is the common ratio between terms

Given sequence:

-8 , -40 , -200 , -1000 , ..

$a_1 = -8$

$r = \frac{-40}{-8} = 5 \\\\r = \frac{-200}{-40} = 5 \\\\r = \frac{ -1000 }{-200 } = 5$

Thus, common ratio, r = 5

Substituting the values we get,

$a_n = (-8) \times 5^{n-1}$

Thus the explicit formula is found

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