Step-by-step explanation:
an arithmetic sequence is a sequence of terms, where every term is created by adding a certain constant to the previous term.
a geometric sequence is when every term is created by multiplying the previous term by a certain constant.
the x coordinate serves as "n" counter of the terms in the sequence.
and the y coordinate is the actual sequence term of that "n".
so, we have
a1 = 4
a2 = 8
a3 = 16
a4 = 32
A)
I think, now it is obvious : the sequence is built by multiplying the previous term by 2.
and this is therefore a geometric sequence.
B)
a2 = a1 × 2 = 4×2 = 8 minutes
a3 = a2 × 2 = a1 × 2 × 2 = 4 × 2 × 2 = 4 × 2² = 16 minutes
a4 = a3 × 2 = 16 × 2 = 32 minutes
a5 = a4 × 2 = 32 × 2 = 64 minutes
C)
based on B we see
an = an-1 × 2 = a1 × 2^(n-1) = 4 × 2^(n-1) = 2² × 2^(n-1) =
= 2^(n+1) minutes
therefore
a8 = 2^(n+1) = 2⁹ = 512 minutes