Answer:
a₅ = 96
Step-by-step explanation:
We know that:
a₁ = 6
aₙ = -2*aₙ₋₁
Then we want to find the value of a₅
We can do it in two ways, we can use the relation to find the terms as:
a₂ = -2*a₁ = -2*6 = -12
a₃ = -2*a₂ = -2*(-12) = 24
a₄ = -2*a₃ = -2*24 = -48
a₅ = -2*a₄ = -2*(-48) = 96
Then we have a₅ = 96
And we know that this is a geometric sequence, where the ratio between terms is -2, then the n-th term can be written as:
aₙ = a₁*r^(n - 1)
where r is the ratio, in this case, r = -2 and a₁ = 6
Then:
aₙ = 6*(-2)^(n -1)
then:
a₅ = 6*(-2)^(5 - 1) = 6*(-2)^4 = 96
