Question

Question

Answer 1

Answer:

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

Step-by-step 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