Question

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The sum of three numbers in G.P . is 14. If the first two terms are each increased by 1 and the third term is decreased by 1 , the resulting numbers are in A.P . Find the product of these three numbers.
a) 125
b) 64
c) 216
d) 124​

Answer 1

Answer:

Taking a common we get, a(1+r+r2)=14⋯⋯⋯(1). We are given that if the first two terms are increased by 1 and the third term is decreased by 1, then they form an arithmetic progression. Third number: ar2−1 . Hence we can say that a, ar+1, ar2−1 are in arithmetic progression.