Find the sum of all the 11 terms of an AP whose middle most term is 30.

Explanation

Since, the total number of terms`(n)=11 " " ` [odd]
` :. ` Middle most term`=((n+1))/(2)"th term"=((11+1)/(2))`th term = 6th term
Given that, `a_(6)=30`
`implies a+(6-1)d=30`
`implies a+5d=30 " " `…(i)
` :' ` Sum of n term of an AP, `S_(n)=(n)/(2)[2a+(n-1)d]`
` :. S_(11)=(11)/(2)[2a+(11-1)d]`
` " " =(11)/(2)[2a+10d]=11(a+5d) " " `[from Eq. (i)]
` " "=11xx30=330`