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

`a_(n)` = 8n + 34

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

34 + 8n

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