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.

A.. 25, 45.......500
B. 20, 33,.., 332
C. 13, 33, , 488
D. 13, 33, ..., 493

Answer 1

Answer: Option 'D' is correct.

Explanation:

Since we have given that

First term = 13

Increase each time = 20

Number of clients = 25

So, it forms an arithmetic progression:

So, 25 th term would be

`a_(25)=a+(n-1)d\\\\a_(25)=13+(25-1)* 20\\\\a_(25)=13+24* 20\\\\a_(25)=13+480\\\\a_(25)=493`

Hence, list would look like 13,33,............493.

Therefore, Option 'D' is correct.