Convert the recursive form a1=5, an=2an−1a1=5, an=2an−1 to the explicit form. (1 point) Responses an=3(7)nan=3(7)nA sub n is equal to 3 times 7 to the n th power an=5(2)n+1an=5(2)n+1A sub n is equal to 5 times 2 raised to the n plus 1 power an=5(2)n−1an=5(2)n−1A sub n is equal to 5 times 2 raised to the n minus 1 power an=2(5)n−1

1 answer

To convert the recursive form a1=5 and an=2an1 into an explicit form, we can calculate the first few terms:

  • a1=5
  • a2=2a1=25=10
  • a3=2a2=210=20
  • a4=2a3=220=40

It appears that the terms are multiplying by 2 each time. Let's notice the pattern:

  • a1=5
  • a2=521
  • a3=522
  • a4=523

From this, we can conclude that in general:

an=52n1

So the explicit form of the sequence is:

an=52n1

Therefore, the correct response is:

an=5(2)n1