## If a , b ,c are in A. P, then a + c = ________.

Question

If a , b ,c are in A. P, then a + c = ________.

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3 weeks 2021-09-06T05:19:38+00:00 2 Answers 0 views 0

1. Given a , b , c are in A.P , then a + c = 2b

General terms of an A.P are a , a+d , a+2d

denote these terms by a , b , c such that

a = a , b = a + d , c = a + 2d

Now we should find a + c

Since a + d is equal to b ,

AP – a, b, c

a+c

## Solution:–

a= a1

b= a1+d

c= a1+ 2d

a+ c = a1+(a1+2d)

= a1+a1+2d

= 2 a1 + 2d

= 2( a1+ d)

since a1 = a

therefore ,

### a+c = 2 (a+d)

since a+d = b

therefore ,