n arithmetic means are inserted between 3 and 17. If the ratio of first to last mean is 1 : 3, then n is equal to:

Let the n arithmetic means between 3 and 17 be A1, A2,…, An If d is the common difference, then,d=17−3n+1=14n+1Also, A1An=13⇒3+d17−d=13⇒ 3+14/(n+1)17−14/(n+1)=13⇒3n+1717n+3=13⇒n=6