the sum of 5th and 9th term of an ap is 8 and their product is 15 find the sum of first 28 terms of the AP
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a5 + a9 =8 = a+4d+ a+ 8d
2a+ 12d=8.
a + 6d= 4. (1) eq
squaring eq 1
a^2 +36d^2+ 12ad = 16
a5*a9 = 15
( a+4d)(a+8d) =15
a^2 + 32d^2 + 12ad= 15. eq 2
solving both equations
d = +-1/2
when d =1/2
a = 1
sum = ( n/2) (2a + (n -1) d)
sum of 28 terms = 217
when d = -1/2
a=7
sum will be 7
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