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
