Question

What are the explicit and recursive formulas for the sequence `6, 10, 14, 18`?

Answer 1

Explicit formula of the sequence is `T_n= 4 n+2`
Recursive formula is `a_1=6,a_n=a_(n-1)+4`

Explanation:

Sequence is `S= {6,10,14,18} ; a= 6 , d= 10-6=4`

Explicit formula gives value of the specified term,

`T_n= a+(n-1)d ; a , d , n` are 1st term, common difference

and position of the term. `T_1= 6+(1-1)4=6`, similarly

`T_4= 6+(4-1)4=6+12=18` Therefore explicit formula

of the sequence is `T_n= 6+(n-1)4=4 n+2`

Recursive formula gives value of the specified term based on

previous term. `a_1= 6 , a_n=a_(n-1)+4 :. a_2=a_(2-1)+4`

or `a_2=a_1+4=6+4=10 ; a_3=a_2+4=10+4=14`

and so on. Therefore , recursive formula of the sequence is

`a_1=6,a_n=a_(n-1)+4` [Ans]