Question

A

Find the recursive definition
of this sequence.
3, 10, 17, 24
an = an-1 + 10
a1 = 3
B
an = 10an-1
a₁ = 3
C
an = an-1+7
a₁
a₁ = 3

Answer 1

Hello! Here are the recursive definitions of the given sequence:

A) The sequence is increasing by 7 for each term, so the recursive definition can be written as:

a1 = 3

an = an-1 + 7

So, the recursive definition of the sequence is: 3, 3+7=10, 10+7=17, 17+7=24, ...

B) The second option given, "anan-1 + 10 a1 = 3" is not a recursive definition of the sequence.

C) The third option given, "San = 10an-1" is also not a recursive definition of the sequence because it uses a different variable 'S' instead of 'a'.