Question

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

Answer 1

Answer:

Given:-

AP - a, b, c

To find :-

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 ,

a+c= 2b

Answer 2

$\huge\blue{\bold{\underline{\underline{AnsWer:-}}}}$

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

$\huge\color{teal}{\bold{\underline{\underline{Verification:-}}}}$

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

$\large\rm{\rightarrow{a+c\:=\:a+a+2d}}$

$\large\rm{\rightarrow{a+c\:=\:2a+2d}}$

$\large\rm{\rightarrow{a+c\:=\:2(a+d)}}$

Since a + d is equal to b ,

$\large\rm{\rightarrow{a+c\:=\:2b}}$

$\huge\rm\bold{\boxed{Hence\:\:\:verified}}$