Question

Find the first term and the explicit formula a12=1/32 and r=1/2

Answer 1

see explanation

Explanation:

The n th term of a geometric sequence is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

Given
`a_(12)` =
`(1)/(32)` and r =
`(1)/(2)`, then

a
`((1)/(2)) ^(11)` =
`(1)/(32)`, that is

`(a)/(2^(11) )` =
`(1)/(32)`

`(a)/(2048)` =
`(1)/(32)` ( cross- multiply )

32a = 2048 ( divide both sides by 32 )

a = 64 ← first term

Thus the explicit formula is

`a_(n)` = 64
`((1)/(2)) ^(n-1)`