Sum

If a, b and c are in A.P show that: a + 4, b + 4 and c + 4 are in A.P.

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#### Solution

a, b and c are in A.P

=> b - a = c - b

=> 2b = a + c

Given terms are (a + 4), (b + 4) and (c + 4)

Now (b + 4) - (a + 4)= b - a

`= (a + c)/2 - a`

`= (a + c - 2a)/2`

`= (c - a)/2`

And (c + 4) - (b + 4) = c - b

`= c - (a + c)/2`

`= (2c - a - c)/2`

`= (c - a)/2`

Since (b + 4) - (a + 4) = (c + 4) - (b + 4), then given terms are in A.P

Concept: Arithmetic Progression - Finding Their General Term

Is there an error in this question or solution?

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