Answer
1. The explicit formula is A(n)=-10+4(n-1). The relationship between the first and second, and then second and third is that the magnitude of the values differs by 4 in each scenario and the previous term is less by 4.
2. The recursive formula is A(n)=A(n-1)+4; A(1)=-10
Work Step by Step
A(n)=-10+4(n-1)
1.
First term --> A(1)=-10+4(1-1) = -10+4(0) = -10
Second term --> A(2)=-10+4(2-1) = -10+4(1) = -10 +4 = -6
Difference by 4 as first term is 4 less than second term
2.
Second term --> -6
Third term --> A(3)=-10+4(3-1) = -10+4(2) = -10 +8 = -2
Difference by 4 as second term is 4 less than third term
4. The recursive formula is A(n)=A(n-1)+4; A(1)=-10
Because the sequence is in the form of A(n)=A(n-1)+d and the value of A(1) is -10 which was derived using the explicit formula. The A(n-1) allows to find the value of previous term and the value of d which is 4 derived from the explicit formula is added to the previous term to find the value of the nth term.
