Question

the sum of four consecutive no in an ap is 32.and the ratio of their first and last term is og the product of middle term is 7ratio 15.find the no

Answer 1

Hey !!!

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Here is your answer

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Let the four consecutive numbers in AP be a-3d,a-d,a+d,a+3d.

So,
      a-3d+a-d+a+d+a+3d=32

       4a=32

      a=8

      (a-3d)(a+3d) / (a-d)(a+d)=7/15

      15(a2-9d2) = 7(a2-d2)

     15a2-135d2 = 7a2-7d2

      8a2-128d2 = 0

       d2 = 4, ±2

Therefore d=4  or d=±2 1mark

So, when a=8 and d=2, the numbers are 2,6,10,14.

When a=8,d=-2 the numbers are 14,10,6,2

Answer 2

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