A sequence of numbers a1 , a2 , a3 , … is defined as follows: a1 =3, a2 = 5 and every term in the sequence after a2 is the sum of all terms in the sequence preceding it, e.g., a3 = a1 + a2 and a4 = a1 + a2 + a3 If an = t and n > 2, then what is the value of an+2 in terms of t ?
a. 8 + t
b. 8t
c. 4t
d. t^3
e. t^4
a_n = a_1 + a_2 + \ldots +a_{n-1} = t
a_{n + 1} = \underbrace{a_1 + a_2 + \ldots +a_{n - 1}}_t + \underbrace{a_n}_t = 2t
a_{n + 2} = \underbrace{a_1 + a_2 + \ldots + a_n}_{2t} + \underbrace{a_{n + 1}}_{2t} = 4t