The sum of 5th and 9th terms of an A.P. is 8 and their product is 15. Find the sum of first 28 terms of the A.P.
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Explanation:
5/2 { 2a + 4d } + 9/2 { 2a +8d }
5a +10 d + 9a + 36d = 8
14a + 46d = 8
7a + 23d = 4
{5a + 10 d } { 9a + 36d } = 15
45a^2 + 180ad + 90ad + 36d^2 = 15
45a^2 + 270ad + 36d^2 = 15
15a^2 + 90ad + 12d^2 = 5
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ans= 217
a+4d+a+8d=8
2a+12d=8
a+6d=4
(a+4d)(a+8d)=15
(4-6d+4d)(4-6d+8d)=15
(4-2d)(4+2d)=15
d=1/2
a+6d=4
a=1
S28=14[2+27/2]
=14(2+13.5)
=14(15.5)
=217
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