Not able to understand the explanation of following question.

Q

An arithmetic progression of n ( n 25 ) terms has only integers in it. The average of the first four terms is 14 and the average of the last four terms is 52. What is the common difference?

A

1

B

2

C

18

D

19

Explanatio…

Question

Not able to understand the explanation of following question.

Q

An arithmetic progression of n ( n > 25 ) terms has only integers in it. The average of the first four terms is 14 and the average of the last four terms is 52. What is the common difference?

A

1

B

2

C

18

D

19

Explanation

Let the first term be a and common difference be d. The average of the first four terms is a+1.5d = 14. The average of the last 4 terms is a+(n-2.5)d = 52. Subtracting, we get, (n-4)d = 38. Since n>25, the only possibility is n-4 = 38 and d = 1.

Akhilesh Singh · Answer

Hi AkshayLet the first four terms of the AP be a, a+d, a+2d, a+3d. On finding the average, we get a+1.5d = 14Similarly let the last 4 terms be a + (n-1)d, a+(n-2)d + a+(n-3)d + a+(n-4)d. The average of these terms would be a + (n-2.5)d. We have been given that this average is equal to 52. a+(n-2.5)d = 52Subtracting the two equations we get(n-4)d = 38n > 25, 38 = 38*1, 19*2Since n>25, so n can only be 42. Hence the common difference would be 1.Hope that makes it clear.Thanks.

Join CAT 2026 course by 5-Time CAT 100%iler

Download resources