Find the sum of the first five terms of the geometric series 50 + 25 + 12.5 +

The sequence is geometric with first term  

a

1

=

100

and common ratio  

r

=

0.5

Explanation:

a

1

=

100

,

a

2

=

50

,

a

3

=

25

,

a

4

=

25

2

,

a

5

=

25

4

...

50

100

=

0.5

,

25

50

=

0.5

,

25

2

25

=

0.5

,

25

4

25

2

=

0.5

∴

a

2

a

1

=

a

3

a

2

=

a

4

a

3

=

a

5

a

4

=

0.5

The ratio of successive term and preceeding term is constant

(

r

=

0.5

)

. Therefore the sequence is geometric whose first

term is  

a

1

=

100

and common ratio is  

r

=

0.5

[Ans]

c) the median for town a 30" is greater than the median for town b 25"

step-by-step explanation:

town a, median = q2 = 30

town b, median - q2 = 25

so the median for town a 30" is greater than the median for town b 25"