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Let the three terms in A.P. be a – d, a, a + d.
given that a – d + a + a + d = 21
a = 7
then the three term in A.P. are 7 – d, 7, 7 + d
According to given condition 9 – d, 9, 21 + d are in G.P.
(9)2 = (9 – d) (21 + d)
81 = 189 + 9d – 21d – d2
81 = 189 – 12d – d2
d2 + 12d – 108 = 0
d(d + 18) – 6 (d + 18) = 0
(d – 6) (d + 18) = 0
We get, d = 6, –18
Putting d = 6 in the term 7 – d, 7, 7 + d we get 1, 7, 13.
Three positive number whose sum is 21 are in arithmetic progression. If 2, 2, 14 are added to them respectively then resulting numbers are in geometric progression. Then which of the following is not among the three numbers?
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