please help I really don.t get it at all pleas help

Question



Enter a recursive rule and an explicit rule for the arithmetic sequence. Then, find the 20th term of the sequence.

25, 35, 45, 55, ...

The recursive rule is f(1) = _____ , f(n) = f (n or n+1 or n-1) +______

The explicit rule is f(n) = ______ +________ (n+1 or n-1 or n)

f(20) = _______

Answer 1

Joseph

Mark is correct above but for the recursive formulation (line 2) you also need a₁=25.

I will give a solution in terms of the notation used in the question also.

Recursive rule : f(1) = first term = 25.

Obviously to go from one term to the next we add 10. So to go from (n-1)st term to the nth we add 10.

So f(1) = 25, f(n) = f(n-1) + 10.

Explicit.

f(n) = f(1) + d (n-1). d = 10 here, f(1) = 25, so 25 + d (n-1).

To find f(20) you just substitute n=20 into the explicit formulation.

Mike

Answer 2

d = 10

a_n+1 = a_n + 10

a_n = 25 + (n - 1)(10)

a₂₀ = 25 + (19)(10)