A sequence with a_1 = 1 is defined by the recurrence relation a_{n + 1} = 2^{n} a_n for all natural numbers n. If a_{23} = 2^p, then what is p?
a1 = 2^0
a2 = 2^1 * 1 = 2^1
a3 = 2^2 * 2^1 = 2^3
a4 = 2^3 * 2^3 = 2^6
a5 = 2^4 * 2^6 = 2^10
a6 = 2^5 * 2^10 = 2^15
.......
The nth term is given by 2 ^ ( n * (n-1) / 2)
a23 = 2 ^ (23 * 22 / 2) = 2^(23 * 11) = 2^253 ⇒ p = 253