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in Arithmetic Progression by (71.6k points)
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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.

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Best answer
given:
a+2d+a+6d=6
a+3d=3
a=3-3d-(1)
(a+2d)(a+6d)=8
`a^2+6ad+8d^2=8`
from equation 1
`(3-3d)^2+6(3-3d)d+8d^2=8`
solving this d=`pm1`
if d=1 then a=0
if d=-1 then a=6
if d=1
`S_n=n/2(2a+(n-1)d)`
`S_16=16/2(2(0)+(15)(1))`
`S_16=120`
if d=-1
`S_16=16/2(2(6)+(15)(-1))`
`s_16=-24`

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