Question

In a geometric sequence {an}, if a1 = 4 and r = 0.2, the first 4 terms in the sequence are
Responses
A {4, .8, .16, .032,...}.{4, .8, .16, .032,...}.
B {4, 20, 100, 500,...}.{4, 20, 100, 500,...}.
C {4, 4.2, 4.4, 4.6,...}.{4, 4.2, 4.4, 4.6,...}.
D {4, 3.8, 3.6, 3.4,...}.

Answer 1

In a geometric sequence, each term is found by multiplying the previous term by a common ratio \( r \).

For the given sequence where \( a_1 = 4 \) and the common ratio \( r = 0.2 \), the first four terms can be calculated as follows:

1. \( a_1 = 4 \)
2. \( a_2 = a_1 \cdot r = 4 \cdot 0.2 = 0.8 \)
3. \( a_3 = a_2 \cdot r = 0.8 \cdot 0.2 = 0.16 \)
4. \( a_4 = a_3 \cdot r = 0.16 \cdot 0.2 = 0.032 \)

Thus, the first four terms of the sequence are \( \{4, 0.8, 0.16, 0.032\} \).

The correct response is:
A \( \{ 4, 0.8, 0.16, 0.032, ... \} \)