If a_0=7 and a_(n+1)=a_n+12 for n>=0, how do you find the values of a_5?

Hallie Stanton

Hallie Stanton

Answered question

2022-11-18

If a 0 = 7 and a n + 1 = a n + 12 for n 0 , how do you find the values of a 5 ?

Answer & Explanation

ebizsavvy1txn

ebizsavvy1txn

Beginner2022-11-19Added 14 answers

This recursive definition describes an arithmetic sequence with initial term 7 and common difference 12.
The general term of an arithmetic sequence can be written:
a n = a + d ( n - 1 )
where a is the initial term and d the common difference.
So in our example, a=7, d=12 and:
a 5 = a + d ( 5 - 1 ) = a + 4 d = 7 + 4 12 = 7 + 48 = 55

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