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

Recursive Formula: a_n = a_n-1 + d

Explicit Formula: a_n = a₁ + d(n - 1)

25, 35, 45, 55, ...

Recursive Formula: f(n) = f(n - 1) + 10, f(1) = 25

Explicit Formula: f(n) = f(1) + 10(n - 1) = 25 + 10n - 10 = 10n + 15

f(20) = 10(20) + 15 = 200 + 15 = 215

Use the explicit formula to find the 20^th term of the sequence. The value of the 20^th term is 215.

Answer 2

Since the first term is 25, a(1) = 25. We're adding 10, right? Since f(2) is f(1) + 10, we have a(n - 1) + 10, meaning the 4th term is the 3rd term plus 10.

How can we get to 25 from 1 and 35 from 2? Well, 1(10) + 15 = 25 and 2(10) + 15 = 35, soooo...

f(n) = 10n + 15

f(20) = 10(20) + 15 = your answer