Answer: 1/8
Step-by-step explanation: The given series is a geometric sequence where each term is obtained by multiplying the previous term by 1/2.
Starting with 2:
2
×
1
2
=
1
2×
2
1
=1
1
×
1
2
=
1
2
1×
2
1
=
2
1
1
2
×
1
2
=
1
4
2
1
×
2
1
=
4
1
So, the pattern shows that each term is obtained by multiplying the previous term by 1/2. Therefore, the next term in the series would be obtained by multiplying the last term (
1
4
4
1
) by 1/2:
1
4
×
1
2
=
1
8
4
1
×
2
1
=
8
1
Therefore, the next number in the series should be
1
8
8
1
.
