Question

For the recursive definition, find an explicit formula that represents the same sequence.A(n) = A(n − 1) + 10; A(1) = 12
a. A(n) = 10n + 2
b. A(n) = 10A(n − 1) + 2
c. A(n) = 2n + 10
d. A(n) = 2A(n − 1) + 10

Answer 1

hello : 
.A(n) = A(1) +(n-1)d   (general term of arithmetic secquence)
d : common difference     A(1) : the first term 
A(n) = 12+(n-1)(10)....A(1) = 12    d = 10
A(n) = 12 +10n -10
A(n) = 10n+2......( answer : a. A(n) = 10n + 2 )