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

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    0
    2021-09-06T05:21:16+00:00

    \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}}

    0
    2021-09-06T05:21:21+00:00

    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

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