Please help with math?

Question

Please show every step and explain

Find the first 6 terms given by the formula tn=tn-1+2tn-2 where t1=2 and t2=5

Answer 1

The first two terms are 2 and 5.

The next term, t3 (so n=3) would be t(3-1) + 2t(3-2) = t2 + 2*t1 = 5 + 2*2 = 9.

The next term is n=4, so continue from here to find the next few terms.

Answer 2

t[n] = t[n-1] + 2 t[n-2] with t[1] = 2 and t[2] = 5

t[3] = 9 (5 + 2*2)
t[4] = 19 (9 + 2*5)
t[5] = 37 (19 + 2*9)
t[6] = 75 (37 + 2*19)