if a1=7 and an=3an-1+3, What is the value of a5

Answer 1

Denise G. gave a completely valid answer.

Just for sake of education and completeness:

This is a linear difference equation, the general solution of which is

u_n=(3/2)(3ⁿ-1)+7*3ⁿ where the subscript starts at 0, i.e. the first term is u₀=7.

Answer 2

a_n=3a_n-1+3

a₁=7

a₂=3a₁+3=21+3=24

a₃=3a₂+3=3(24)+3=75

a₄=3a₃+3=3(75)+3=228

a₅=3a₄+3=3(228)+3 = 687

Answer 3

a₁=7

a₂=3a_n-1+3 This means:

a₂=3a_2-1+3

a₂=3a₁+3 Now can plug in values

a₂=3(7)+3 = 24 Following the same pattern

a₃=3a₂+3 = 3(24)+3 = 75

a₄=3a₃+3 = 3(75)+3 = 228

a₅=3a₄+3 = 3(228)+3 = 687