the four terms are
a, a+d, a+2d, a+3d
their sum = 72
4a + 6d = 72
2a + 3d = 36 **
product of extremes: a(a+3d)
product of means: (a+d)(a+2d)
a(a+3d) / (a+d)(a+2d) = 9/10
10a^2 + 30ad = 9a^2 + 27ad + 18d^2
a^2 + 3ad - 18d^2 = 0
(a + 6d)(a - 3d) = 0
a = -6d or a = 3d ***
if a = 3d, in **
2(3d) + 3d = 36
9d = 36
d = 4 , then a = 12
and the terms are 12, 16, 20, 24
if a = -6d in **
2(-6d) + 3d = 36
-9d = 36
d = -4 , a = 24
terms are : 24, 20, 16, 12
notice the terms are just in reverse order
Find four consecutive terms in A.P whose sum is 72 and the ratio of product of the extreme terms to the product of means is 9:10
6 answers
four consecutive terms are a-3d , a-2d, a+2d , a+3d
sb high school jalna
excellent
Thanks a lot!
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