Question

Question

Enter a recursive rule and an explicit rule for the arithmetic sequence. Then, find the 20th term of the
sequence
55, 65, 75, 85,-
The recursive rule is f(1) =
f(n)=f(?
+
The explicit rule is f(n) =
+
?
f(20) =

Answer 1

The recursive rule is
`f(1)` = first term;
`f_({n})` =
`f_({n-1})` + d

f(1) = 55;
`f_(20)` =
`f_(19)` + 10

The explicit rule is f(n) = f(1) + (n - 1)d

f(20) = 245

Explanation:

The recursive rule of the arithmetic sequence is

`a_(1)` = first term;
`a_(n)` =
`a_(n-1)` + d

Where:

• 
  `a_(1)` is the first term in the sequence

• 
  `a_(n)` is the nth term in the sequence

• 
  `a_(n-1)` is the term before the nth term

• n is term number

• d is the common difference.

The explicit rule of the arithmetic sequence is

`a_(n)=a_(1)+(n-1)d`

where:

• 
  `a_(1)` is the first term in the sequence

• 
  `a_(n)` is the nth term in the sequence

• n is term number

• d is the common difference

∵ The first 4 terms of the sequence are 55, 65, 75, 85

∴
`a_(1)` = 55

∵ d = 65 - 55

∴ d = 10

∵ We need to find the 20th term

∴ n = 20

∵ The recursive rule is
`f(1)` = first term;
`f_({n})` =
`f_({n-1})` + d

→ Substitute the values of
`a_(1)`, n, and d in recursive rule

∴ f(1) = 55;
`f_(20)` =
`f_(19)` + 10

∵ The explicit rule is f(n) = f(1) + (n - 1)d

→ Substitute the values of n and d to find it

∴ f(20) = 55 + 19(10) = 245

∴ f(20) = 245