Find the eighth term of the geometric sequence, given the first term and common ratio

Question

a₁=6 and r=-1/3

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Answer 1

use the formula a_n=a₁r^(n-1)

a₈=6(-1/3)⁷

a₈=6(-1/3)(-1/3)⁶

a₈=(-2)(-1/3)⁶

a₈=(-2)(1/729)

a₈=-2/729

Answer 2

The formula for the n^th term is:

a_n = a₁r^n-1

where a_n = n^th term of the sequence

a₁ = first term of the sequence

r = common ratio

For this problem,

n = 8, so we want to find a₈

a₁ = 6

r = -1/3

a₈ = 6(-1/3)^8-1

a₈ = 6(-1/3)⁷

a₈ = 6(-1)⁷/3⁷

a₈ = 6(-1)/3⁷

a₈ = -2/3⁶

a₈ = -2/729

Answer 3

You just need to plug-in numbers into the n-th term of geometric sequence:

a_n = a₁ r^n-1

^{For n=8 we will get}

a₈ = 6 * (-1/3)^8-1 = - 0.00274