Question

which sequence is equivalent to t(n)=3+6n, where n>1

Answer 1

It would probably be helpful if you posted the answers provided. Anyway, this sequence would look like this: (You just have to plug n = 2 into the equation and then for the next term plug in n=3 and so on and so on)

15, 21, 27, 33, 39, 45, ....

Answer 2

Theses are the answers
a.
t(1) = 9; t(n + 1) = t(n) + 6
b.
t(1) = 3; t(n + 1) = t(n) + 6
c.
t(1) = 9; t(n + 1) = 6t(n)
d.
t(1) = 3; t(n + 1) = 6t(n)

Answer 3

Well t(1) = 3 + 6*1 = 9.
Also, t(n+1) = t(n) + 6 is obviously true as this is equivalent to t(n+1) -t(n) = 6. Now if we look at our sequence

t(n+1) = 3 + 6(n+1) = 3 + 6n + 6
t(n) = 3 + 6n

So, t(n+1) - t(n) = 3 + 6n + 6 - (3 + 6n) = 3 + 6n - 3 - 6n + 6 = 6.

Hence, a is the correct answer