Question

Please help me out with this!

Keisha made a conjecture about this sequence: 2, 4, 8, ... Keisha’s conjecture: Since 8 is 2 x 4 the pattern is to multiply the previous two elements together to get the next element. Therefore the next element would be 4 x 8 = 32

Evaluate Keisha’s reasoning and create a different conjecture for this sequence.

Answer 1

we know that
Keisha’s reasoning
to create the sequence we are going to need the first two terms, so if we only have the first term, we can not calculate the sequence

Personal conjecture
let
a1=2
a2=4
a3=8
a4=?
a2/a1=4/2------> 2--------> a2=a1*2
a3/a2=8/4------> 4--------> a3=a2=2
so
this is a geometric sequence with a common ratio of 2
a4=2*a3-------> a4=2*8------> a4=16