Question

How do you write the first five terms of the geometric sequence `a_1=1, r=1/2`?

Answer 1

`1, 1/2,1/4,1/8,1/16`

Explanation:

Geometric sequences are defined by the formula `ar^(n-1)` where `a` is the first term and `r` is the common ratio (i.e. the second term divided by the first term or third divided by second).

When `n=1`, `ar^(n-1)` becomes `1times(1/2)^(1-1)=1times1` (anything to the power of zero is one).

When `n=2`, `ar^(n-1)` becomes `1times(1/2)^(2-1)=1times1/2` and so on.

Answer 2

`1,1/2,1/4,1/8,1/16`

Explanation:

`"the standard terms of a geometric sequence are"`

`a,ar,ar^2,ar^3,........ ,ar^(n-1)`

`"where a is the first term and r the common ratio"`

`"to obtain a term in the sequence multiply the previous"`
`"term by r"`

`"here "a=a_1=1" and "r=1/2`

`a_1=1`

`a_2=1xx1/2=1/2`

`a_3=1/2xx1/2=1/4`

`a_4=1/4xx1/2=1/8`

`a_5=1/8xx1/2=1/16`