Question

For each sequence defined recursively, write the first few terms. Then use the terms to write an explicit equation.

a(1)=17 a(n+1)=a(n)-3

And

a(1) =20. a(n+1)=1/2*a(n)

Answer 1

a(1)=17 a(n+1)=a(n)-3
a(2) = a(1) - 3 = 17-3 = 14
a(3) = a(2) - 3 = 14-3 = 11
decreases by 3 each time, ? - 3 = 17

looks like a(n) = -3n+ 20

a(1) =20. a(n+1)=1/2*a(n)
a(2) = (1/2) a(1) = 10
a(3) = (1/2) a(2) = 5

so 20, 10, 5 <---- a GS with a = 20 r = 1/2
t(n) = ar^(n-1)
t(n) = 20 (1/2)^(n-1)