Write a recursive rule an explicit rule for the geometric sequence 12, 3, 3/4, 3/16

Step-by-step explanation:

Recursive Rule

For a geometric sequence with first term a1 and common ratio r, the recursive rule is always ...

  a[n] = r×a[n-1], a[1] = a1

For your first term a1 = 12 and common ratio r = 1/4, the recursive rule is ...

  a[n] = (1/4)×a[n-1], a[1] = 12

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Explicit Rule

For the same geometric sequence, the explicit rule is ...

  a[n] = a1×r^(n-1)

For your sequence, the explicit rule is ...

  a[n] = 12×(1/4)^(n-1)

8

step-by-step explanation:

just put √(2) * √(32) into a calculator. that will make the answer be 8.