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Common Difference

If a, b and c...

Question

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

(i) 4a , 4b and 4c are in A.P.

(ii) a + 4, b +4 and c + 4 are in A.P.

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Solution

a) a, b and c are in A. P
Therefore b-a=c-b
Similarly
4b-4a=4c-4b
4(b-a)=4(c-b)
b-a=c-b
Hence proved

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

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

a + 4, b +4 and c + 4 are in A.P.
because a, b, c are in A. P

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