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Sum of first 55 terms in an A.P.is 3300,...

Sum of first 55 terms in an A.P.is 3300,find its `28^( th )` term.

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The correct Answer is:
The 28th term is 60.
`S_(n)=S_(55)=3300`.
Let the first term of the A.P. Be a common difference d.
`S_(n)-(n)/(2)[2a+(n-1)d]` …(Formula)
`thereforeS_(55)=(55)/(2)[2a+(55-1)d]=(55)/(2)[2a+54d]`
`thereforeS_(55)=55(a+27d)`
`therefore3300=55(a+27d)` ...(Given :`S_(35)=3300)`
`therefore(3300)/(55)=a+27d` ...(Dividing both sides by 55)
`therefore60=a+27d` ...(1)
Now, the 28th term is `t_(28)`
`t_(n)=a+(n-1)d` ...(Formula)
`thereforet_(28)=a+(28-1)d`
`=a+27d`.
But, `a+27d`. ...[From(1)]
`thereforet_(28)=60`
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