the sum of 3rd and the 7th term of an ap is 6 and their product is 8 find the first term and the common difference of an ap
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Step-by-step explanation:
(a+2d) + (a+6d) = 6
2a+8d = 6
a+4d = 3
a = 3-4d
(a+2d)(a+6d) = 8
a^2+8ad+12d^2 = 8
(3-4d)^2 + 8(3-4d)d + 12d^2 = 8
9-24d+16d^2 + 24d-32d^2 +12d^2 = 8
1-4d^2 = 0
1 = 4d^2
1/4 = d^2
(1/2)^2 = d^2
d = 1/2
=>> a = 3-4(1/2) = 3-2 = 1
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