If1,A1,A2,A3,....An,31 are in A.P. and A7:An-1=5:9 then n
28
14
15
13
Explanation for correct option:
Finding the value of n:
Given ,1,A1,A2,A3,...An,31 are in A.P.
So 1+n+1d=31 as there are n+2 terms
⇒d=30n+1...i
A7:An-1=5:91+7d1+n-1d=59
Substitute d in above equationi
1+730n+11+n-130n+1=59⇒n+1+210n+1n+1+n-130n+1=59⇒n+211n+1n+1+30n-30n+1=59⇒n+211(31n-29)=59⇒n+2119=5(31n-29)⇒9n+1899=155n-145⇒9n-155n+1899+145=0⇒-146n+2044=0⇒2044=146n⇒n=2044146⇒n=14
Hence option(B) is correct.