Explanation:
16, 48, 144
hmmm.
the first thing that comes to mind : it cannot be an addition, as the difference between the 2nd and 3rd numbers is much bigger than the difference between the 1st and 2nd numbers.
so, we try multiplication.
and I see : 16×3 = 48
aha !
48×3 = 144
ok, we found it. the sequence is clearly created by multiplying always the previous number by 3.
so, we have 2 main choices to get the 6th term :
1. simply calculate 144 ×3×3×3 (3 times to get from the 3rd to the 6th term).
2. define the sequence formula and calculate for the 6th term.
1.
144 × 3×3×3 = 144 × 27 = 3,888
2.
a1 = 16
a2 = a1×3 = 16×3 = 48
a3 = a2×3 = a1×3×3 = 16×9 = 144
an = a1 × 3^(n-1) = 16 × 3^(n-1)
a6 = 16 × 3⁵ = 16 × 243 = 3,888