The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of sixteen terms of the AP.
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Step-by-step explanation:
a₃ + a₇ = 6 and a₃ . a₇ = 8
we know that d is common difference and a is first term
a₃ = a + 2d and a₇ = a + 6d
∴ a₃ + a₇ = a + 2d + a + 6d +
6 = 2a + 8d = 2(a + 4d)
3 = a + 4d
a = 3 - 4d
now a₃ . a₇ = 8
(a + 2d)(a + 6d) = 8
substitute a = 3 - 4d we get
(3 - 4d +2d)(3 - 4d + 6d) = 8
(3 - 2d)(3 + 2d) = 8
9 - 4d² = 8
1 = 4d²
1/4 = d²
d= 1/2
hence a = 3 - 4 . 1/2 = 3 - 2 = 1
AP = 1, 1+1/2, 1+2.1/2.....
AP is 1, 1.5, 2, 2.5.....
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