Answer: a₉ = 327,680
Step-by-step explanation:
This seems to be a geometric sequence.
The recursive relation for this type of sequence is:
aₙ = aₙ₋₁*r
Where r is a constant.
Then we also have:
aₙ/aₙ₋₁ = r.
then we can find the value of r if we take the quotient of different consecutive terms, for example, the quotient of the second and firs term is:
r = 20/5 = 4
And the quotient between the third and second term is:
r = 80/20 = 4
Then we can conclude that r = 4.
And also, the n-th term of this sequence can be written as:
aₙ = a₁*r^(n - 1)
such that:
a₁ = 5
r = 4
Then the n-th term of this sequence is:
aₙ = 5*(4)^(n - 1)
Then the term a₉ can be found if we just replace n by 9 in the above equation:
a₉ = 5*(4)^(9 - 1) = 5*(4)^(8) = 327,580
