Answer: the next three terms are 8, 16 and 32
Step-by-step explanation:
A geometric sequence is a sequence in which each term is obtained by multiplying the preceding term by a common ratio. The formula for the nth term,Tn of a geometric sequence is expressed as
Tn = ar^(n - 1)
Where
r is the common ratio
n is the number of terms
the first two terms of a geometric sequence 2,4. Therefore
a = 2
r = 4/2 = 2
The formula becomes
Tn = 2 × 2^(n - 1)
To determine the third term, n = 3. So,
T3 = 2 × 2^(3 - 1) = 2 × 2^2
T3 = 8
To determine the fourth term, n = 4. So,
T4 = 2 × 2^(4 - 1) = 2 × 2^3
T4 = 16
To determine the fifth term, n = 5. So,
T5 = 2 × 2^(5 - 1) = 2 × 2^4
T4 = 32
