Respuesta :

fieryanswererft

Answer:

aₙ = 4(5)ⁿ⁻¹

Explanation:

To identify a geometric series: second term = √(first term * third term)

Here given:

  • 1st term: 4
  • 2nd term: 20
  • 3rd term: 100

check ============

20 = √(100*4)

20 = √400

20 = 20  Hence its a geometric term.

Find common difference (r):

20/4 = 5       or     100/20 = 5

Geometric term formula:
aₙ = a₁(r)ⁿ⁻¹               [where a1 is the 1st term, r is common difference]

insert values found

aₙ = 4(5)ⁿ⁻¹ ......this is the nth term.

4,20,100

  • First term=a=4

Common ratio

  • r=20/4=5

Now

explicit formula

  • a_n=ar^{n-1}
  • a_n=4(5)^{n-1}