Question

A salesperson obtained a systematic sample of size 20 from a list of 500 clients. to do​ so, he randomly selected a number from 1 to 25​, obtaining the number 16. he included in the sample the 16th client on the list and every 25th client thereafter. list the numbers that correspond to the 20 clients selected.

Answer 1

This is an arithmetical sequence.
First term is
`a_1=16` (the number of first client), the difference is
`d=25` (because every 25th client was selected) and n=20 (20 clients were selected).
Then,

`a_2=16+25=41`

`a_3=41+25=66`

`a_4=66+25=91`

`a_5=91+25=116`

`a_6=116+25=141`

`a_7=141+25=166`

`a_8=166+25=191`

`a_9=191+25=216`

`a_(10)=216+25=241`

`a_(11)=241+25=266`

`a_(12)=266+25=291`

`a_(13)=291+25=316`

`a_(14)=316+25=341`

`a_(15)=341+25=366`

`a_(16)=366+25=391`

`a_(17)=391+25=416`

`a_(18)=416+25=441`

`a_(19)=441+25=466`

`a_(20)=466+25=491`