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Question: If the first, second and the last terms of an A.P. are a, b, c respectively, then the sum is...

If the first, second and the last terms of an A.P. are a, b, c respectively, then the sum is

A
B

(b+c)(a+b−2c)2(b−a)\frac { ( b + c ) ( a + b - 2 c ) } { 2 ( b - a ) }

C

(a+c)(b+c−2a)2(b−a)\frac { ( a + c ) ( b + c - 2 a ) } { 2 ( b - a ) }

D

None of these

Answer

(a+c)(b+c−2a)2(b−a)\frac { ( a + c ) ( b + c - 2 a ) } { 2 ( b - a ) }

Explanation

Solution

We have T1 = a, T2 = b then c.d = b – a

last term = c

n = = c−ab−a+1\frac { c - a } { b - a } + 1 = c+b−2ab−a\frac { c + b - 2 a } { b - a }

Sn = n2\frac { \mathrm { n } } { 2 } (a+ℓ)( a + \ell )

= (b+c−2a)(a+c)2(b−a)\frac { ( b + c - 2 a ) ( a + c ) } { 2 ( b - a ) }