Question

The first, second and middle terms of an A.P. are a, b and c respectively. Their sum is

• A. $\frac { 2 ( c - a ) } { b - a }$
• B. + c
• C. $\frac { 2 c ( b - a ) } { c - a }$
• D. $\frac { 2 b ( c - a ) } { b - a }$

Answer 1

Answer: (B)

+ c

Answer 2

Let the number of terms be 2n + 1

Q middle term = T_n+1 = c; T₁ = a, T₂ = b; d = b – a

a + (n + 1 –1) (b – a) = c

n = $\frac { c - a } { b - a }$

sum of all terms

= [ 2a + (2n +1 –1) (b –a)]

= $\frac { 1 } { 2 }$ $\left[ 2 \left( \frac { \mathrm { c } - \mathrm { a } } { \mathrm { b } - \mathrm { a } } \right) + 1 \right]$

= + c