How many terms of the AP `-15, -13, -11, … ` are needed to make the sum `-55` ?

Explanation

Let n number of terms are needed to make the sum `-55`.
Here, first term (a) `= -15`, common difference (d)`= -13+15=2`
` :' ` Sum of n terms of an AP, `S_(n)=(n)/(2)[2a+(n-1)d]`
`implies55=(n)/(2)[2(-15)+(n-1)2] " "[:' S_(n)= -55 ("given")]`
`implies -55= -15n+n(n-1)`
`implies-55= -15n+n(n-1)`
`impliesn^(2)-16n+55=0`
`impliesn^(2)-11n-5n+55=0 " " ` [by factorisation method]
`implies n(n-11)-5(n-11)=0`
`implies(n-11)(n-5)=0`
` :. n=5, 11`
Hence, either 5 and 11 terms are needed to make the sum`-55`.