Question

please solve 12th and 13th questions !! chapter - arithmetic and geometric progression.

●correct answer.
●20 points !!!

Fast !!☺

Answer 1

Hey there !!!!!!!


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12) a,b,c are in A.P 

          2b = a+c

           b= a+c/2---Equation 1

A B C are said to be in GP if

            B=√AC

here A= 3^a B=3^b C=3^c

           A*C = 3^a*3^c

           AC= 3^(a+c)

       Applying square root on both sides

             √AC= √3^(a+c)

             √AC= 3^(a+c)/2

But from equation 1  a+c/2 = b

              √AC= 3^b = B

              B=√AC

So, 3^a 3^b 3^c are in A.P

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13)  a,b,c are in A.P 

          2b = a+c

           b= a+c/2---Equation 1

A B C are said to be in GP if

            B=√AC

here A= 10^ax+10   B=10^bx+10    C=10^cx+10


        A*C = 10^ax+10*10^cx+10

       AC= 10^(ax+10+cx+10)= 10^( 20+(a+c)x )

       AC=10^( 20+(a+c)x )

      Applying square root on both sides

        √AC=√10^( 20+(a+c)x )

        √AC=10^( (20+(a+c)x) /2)

      √AC=10^( 20/2+(a+c)x /2)

From equation 1 a+c/2 = b

      √AC=10^( 10+(b)x ) = B 

         B=√AC

So   10^ax+10  10^bx+10   10^cx+10 are in G.P 

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Hope this helped you.....................