The sum of the third and the seventh terms of an AP is 6 and their product is 8. find the sum of first sixteen terms of the AP.​

1 thought on “The sum of the third and the seventh terms of an AP is 6 and their product is 8. find the sum of first sixteen terms of the AP.​”

1. Answer:

   given: a+2d+a+6d=6

   2a+8d=6

   2(a+4d)=6

   a+4d=3

   a=3-4d ——(1)

   (a+2d)(a+6d)=8

   putting the value of a

   (3-4d+2d)(3-4d+6d)=8

   (3-2d)(3+2d)=8

   (a-b)(a+ b)=a2-b2

   (3)2-(2d)2=8

   9-4d2=8

   9-8=4d2

   4d2=1

   d2=1/4

   d=√1/4

   d=1/2

   putting this value of d in 1

   a=3-4multiply1/2

   a=3-2

   a=1

   S16=n/2(2a+(n-1)d)

   16/2(2multiply1+(16-1)1/2)

   8(2+15/2)

   8(2+15/2)

   take LCM

   8{(4+15)/4)}

   =38 ANSWER

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