A salesperson obtained a systematic sample of size 2525 from a list of 500500 clients. To do so, he randomly selected a number from 1 to 2020 , obtaining the number 1313. He included in the sample the 1313th client on the list and every 2020th client thereafter. List the numbers that correspond to the 2525 clients selected.

Question

A salesperson obtained a systematic sample of size 25 from a list of 500 clients. To do so, he randomly selected a number from 1 to 20, obtaining the number 13. He included in the sample the 13th client on the list and every 20th client thereafter. List the numbers that correspond to the 25 clients selected.

Answer:

13, 33, 53, ... 393

Step-by-step explanation:

The Question is making reference to arithmetic progression

Where the first term is 13

And the difference between each interval is 20 (i. e number of clients)

Using the following formula, well obtained the client in any position

Tn = a + (n - 1) d

Where Tn = nth term

a = T1 = 1st term = 13

n = number of terms = 1 to 25

d = common difference = 20

Calculating T2

T2 = 13 + (2 - 1) * 20

T2 = 13 + 20

T2 = 33

Calculating T3

T3 = 13 + (3 - 1) * 20

T3 = 53

...

Calculating the 20th term

T3 = 13 + (20 - 1) * 20

T20 = 393