Let the numbers be x-a, x, x+a
∴ For last 3 terms to be in G.P:-
(x+a)^{2} = x(x-a+40)
x^{2}+a^{2}+2ax = x^{2}-ax+40x
a^{2} = -3ax + 40x
=) x =
Now, since x is a positive integer, putting different integral value of a .
Only a = 12 gives a integer value of x = 36
(Note, a=b also give integral value x=b but then the first term becomes 0)
∴ x = 36, a = 12
∴ x – a = 24
x = 36
x+a = 48
x-a+40 = 64
∴ Sum of all the terms = 64+48+36+24 = 172
The terms are - 24,36,48,64
Correct Answer: 172
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