If a,b,c form an AP with common

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Solution

Q.
If a, b, c from an AP with common difference d, then the value of $a - 2 b - c$ is equal to

1 $2 a + 4 d$

2 0

3 $- 2 a - 4 d$

4 $- 2 a - 3 d$

Ans.
(3)

$a, b, c a r e i n A P w i t h c o m m o n d i f f e r e n c e = d ∴ b - a = c - b = d \Rightarrow b - a = d \Rightarrow a = b - d \Rightarrow b = a + d a n d c - b = d \Rightarrow c = b + d \Rightarrow c = a + 2 d N o w, a - 2 b - c = a - 2 (a + d) - (a + 2 d) = a - 2 a - 2 d - a - 2 d = - 2 a - 4 d$

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