# If A, B and C Are in A.P Show That: A + 4, B + 4 and C + 4 Are in A.P. - Mathematics

Sum

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 given terms are in A.P

Concept: Arithmetic Progression - Finding Their General Term
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 10 Arithmetic Progression
Exercise 10 (B) | Q 11.2 | Page 140