Algebra: Arithmetic progression
Find four consecutive terms in an A.P. whose sum is 36 and the product of the 2nd and 4th is 105. The terms are in ascending order..
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let the 4 terms be a - 3d, a-d, a+d and a+3d
Sum = 4a = 36, so a = 9
Product of 2nd and 4th = (9-d)(9+3d)=105
81+27d-9d-3d2 = 105
3d2-18d+24=0
d2-6d+8=0
(d-2)(d-4)=0
so d=2, or 4
numbers are
3, 7, 11, 15
or
-3, 5, 13, 21
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