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Question
If a, b and c are in A.P. show that a + 4, b + 4 and c + 4 are in A.P.
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 the given terms are in A.P.
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