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Not able to understand the explanation of following 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.
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Answer
Hi Akshay
Let the first four terms of the AP be a, a+d, a+2d, a+3d. On finding the average, we get a+1.5d = 14
Similarly 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 = 52
Subtracting the two equations we get
(n-4)d = 38
n > 25, 38 = 38*1, 19*2
Since n>25, so n can only be 42. Hence the common difference would be 1.
Hope that makes it clear.
Thanks.
