Question

If a 1 =6 and a n =-2a n-1 a 5 then find the value of a5

Answer 1

a₅ = 96

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