# Geometric progression

Three numbers whose sum is 15 are in a.p. if 1,4,19 be added to them respectively the resulting number are in g.p find n

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1. Let the original numbers be
a, a+d, and a+2d

3a + 3d = 15 or a+d = 5 ----> d = 5-a

after the addition, the three numbers are:
a+1, a+d+4, and a+2d+19
they are now in GP, that is ....
(a+d+4)/(a+1) = (a+2d+19)/(a+d+4)
(a + 5-a + 4)/(a+1) = (a + 10-2a + 19)/(a + 5-a + 4)
9/(a+1) = (-a + 29)/9
81 = -a^2 + 28a + 29
a^2 - 28a + 52 = 0
(a - 26)(a - 2) = 0

a = 26 or a = 2

if a = 26, then d = 5-26 = -21
and the original 3 numbers were:
26, 5, and 16

if a = 2, then d = 5-2 = 3
and the original 3 numbers were:
2, 5, and 8

Your question was "find n", I will let you figure out what that means.

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2. 2,5,8, or 26,5,-16

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3. Three numbers are in A.P and their sum is 15. If 1,4 and 19 are added to these numbers respectively, the resulting numbers are in G.P .Find the numbers.

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4. how did the difference 9 come

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6. Thankđź™Źđź’• you

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