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Question: Two arithmetic means are inserted between 31 and 64. What is the common difference?


A ) 11
B ) 33
C ) 16
D ) 9

Steps to derive

1 The arithmetic sequence is 31, a2, a3, 64

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

3 a4 = a1 + (4 - 1)d
 [Substitute the values.]

4 64 = 31 + 3d
 [Substitute the values.]

5 33 = 3d

6 11 = d

7 So, the Common difference is 11.



Hence the right answer is Option A

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