Question

the sum of the four consecutive number in an A.P is 32and theratio of the product of the first and the last term of the product of two middle term is 7:15find the number

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

Here it is

the steps are in the above pic

hope it helps u

have a nyc day .