Question

the first term of an arthimetic sequence is 42 the rule an= an-1 +8 can 1 can be used explain how to write explict rules

Answer 1

Answer:

$a_{n}$ = 8n + 34

Step-by-step explanation:

The explicit rule for an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given the recursive rule

$a_{n}$ = $a_{n-1}$ + 8

where + 8 is the common difference d , then

$a_{n}$ = 42 + 8(n - 1) = 42 + 8n - 8 = 8n + 34

Explicit rule is

$a_{n}$ = 8n + 34

Answer 2

Answer:

34 + 8n

Step-by-step explanation:

a₁ = 42

$a_{n} = a_{n-1} + 8$

a₂ = a₁ + 8    = 42 + 8   = 50

a₃ = a₂ + 8   = 50 + 8 = 58

a₄ = a₃ + 8 =   58 + 8  = 66

Arithmetic sequence: 42, 50 , 58 , 66, ......

a₁ = 42 ; d = 8

$a_{n}$ = a₁ + d(n-1)

    = 42 + 8(n - 1)

    = 42 + 8n - 8

   = 34 + 8n