The sum of the 3rd and the 7th terms of an apis 6 and their product is 8. Find the sum of first sixteen terms of the ap.
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a3 + a7 = 6
a + 2d + a + 6d = 6
2a + 8d = 6
a + 4d = 3
a = 3 - 4d
also, (a + 2d) (a+6d) = 8
(3 - 4d + 2d) ( 3 - 4d + 6d) = 8
(3 - 2d) ( 3 + 2d) = 8
9 - 4d^2 = 8
4d^2 = 1
d^2 = 1/4
d = 1/2
we can find value of a
therefore a = 3 - 4 ( 1/2) = 3 - 2 = 1
to find....
s16 = 16/2 (2(1) + (16-1)1/2) = 8 ( 2 + 15/2 ) = 8 ( 19/2) = 76 answer
a + 2d + a + 6d = 6
2a + 8d = 6
a + 4d = 3
a = 3 - 4d
also, (a + 2d) (a+6d) = 8
(3 - 4d + 2d) ( 3 - 4d + 6d) = 8
(3 - 2d) ( 3 + 2d) = 8
9 - 4d^2 = 8
4d^2 = 1
d^2 = 1/4
d = 1/2
we can find value of a
therefore a = 3 - 4 ( 1/2) = 3 - 2 = 1
to find....
s16 = 16/2 (2(1) + (16-1)1/2) = 8 ( 2 + 15/2 ) = 8 ( 19/2) = 76 answer
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