The recursive formula for a sequence is Un=Un-1.+12, where Un is the nth term of the sequence and U0=7. Which explicit formula can be used to determine the nth term of the sequence?
A. 7n+19
B. 7n+12
C. 7+19n
D. 7+12n

Question

loser66 · Answer

$$U_1=U_0+12\U_2=U_1+12=~~~U_0+12+12~=U_0+2*12\U_3=U_2+12=U_0+2*12+12=U_0+3*12\U_4=U_3+12= U_0+3*12+12=U_0+4*12$$..................................................
therefore, $U_n= U_0+n*12=7+12n$