Arithmetic Question

What are are the 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 a_n = a₁ + (n - 1)d
[Use the formula for the n^th 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
[a_{n + 1} = a_n + 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