What is the 6th term of the geometric sequence where a1 = -625 and a2 = 125?

Solution:

The formula to find the nth term of geometric sequence is

a_n = a r^n-1

Where a1 is the first number

r is the ratio

n is the number of terms

It is given that

a = -625

r = 125/-625 = -1/5

n = 6

Substituting it in the formula

a₆ = -625 x (-1/5)^6-1

By further calculation

a₆ = -625 x (-1/5)⁵

a₆ = -625 x (-1/3125)

So we get

a₆ = 1/5

a₆ = 0.2

Therefore, the 6th term of the geometric sequence is 0.2.

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What is the 6th term of the geometric sequence where a1 = -625 and a2 = 125?

Summary:

The 6th term of the geometric sequence where a₁ = -625 and a₂ = 125 is 0.2.