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Show that the sum of an AP whose first t...

Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a+c)(b+c-2a))/(2(b-a))`.

Text Solution

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Le the number of terms in A.P. =n
common difference d=b-a
c=nth term of the A.P.
`rArr c=a+(n-1)(b-a)`
`rArr c-a(n-1)(b-a)`
`rArr n-1=(c-a)/(b-a)`
`rArr n=(c-a)/(b-a)+1=(c-a+b-a)/(b-a)=(b+c-2a)/(b-a)`
`:.` Sum of n term of A.P. `=(n)/(2)(a+l)`
`=((b+c-2a))/(2(b-a))(a+c)=((a+c)(b+c-2a))/(2(b-a))`
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