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Question: What are the three arithmetic means between 24 and 72?


A ) - 36, 48, - 60
B ) 37, 50, 63
C ) 36, 48, 60
D ) 36, - 48, - 60

Steps to derive

1 Given data: a1= 24, a5 = 72

2 The arithmetic sequence is 24, a2, a3, a4 , 72

3 an = a1 + (n - 1)d
 [Use the formula for the nth term.]

4 a5 = a1 + (5 - 1) d
 [Substitute the values.]

5 72 = 24 + 4d
 [Substitute the values.]

6 d = 12

7 a2 = a1 + d = 24 + 12
 [an + 1 = an + d.]

8 a2 = 36.

9 a3 = a2 + d = 36 + 12 = 48

10 a4 = a3 + d = 48 + 12 = 60

11 So, the three arithmetic means are 36, 48, and 60.



Hence the right answer is Option C

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