# If N Arithmetic Means Are Inserted Between 1 And 31 Such That Ratio Of First And Nth Mean Is 3:29, Then What Is The Value Of N?

The first mean = 1 + d

The nth mean = 1 + nd

ration =$\frac{3}{29}$ $\frac{1 + d}{1 + nd} \Rightarrow \frac{3}{29}$—[1]

31 = 1 + (n + 1)d—[2]

By solving both the equations [1] and [2], we get:

n = 14

Therefore, the value of n is 14.

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