Question

. The product of first three terms of a G.P. is 1000. If we add 6 to its second term and 7 to its third term, the resulting three terms form ap then find the terms of gp
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Answer 1

Answer:

Answer : 5,10,20

Explanation:Let the 3 numbers be a/r, a, ar.

a/r ∗a ∗ar =1000

a3=1000

a=10

2(a+6)=(ar+7)+a/r a=10

32r=10r²+7r+10

10r²−25r+10=0

r²−5r+1=0

(r−2)(2r−1)=0r=2,1/2

=5,10,20or20,10,5.

Answer 2

AnswEr:

Let first three terms of the given G.P. be

$\qquad \tt \frac{a}{r} ,a,ar. \sf \: Then,$

$\sf \: Product = 1000 \\ \\ \implies \sf \: {a}^{3} = 1000 \rightarrow \: a = 10$

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• It is given that $\sf\dfrac{a}{r},a+6,\:ar+7\:are\:in\:A.P.$

$\therefore \sf \: 2(a + 6) = \frac{a}{r} + ar + 7 \\ \\ \sf \rightarrow \: 32 = \frac{10}{r} + 10r + 7 \\ \\ \sf \rightarrow \: 25 = \frac{10}{r} + 10r \\ \\ \sf \rightarrow \: 5 = \frac{2}{r} + 2r \\ \\ \sf \rightarrow \: {2r}^{2} - 5r + 2 = 0 \\ \\ \sf \rightarrow \: (2r - 1)(r - 2) = 0 \\ \\ \sf \rightarrow \: r = 2 \: and \: 1/2$

• Hence, the G.P. is 5, 10, 20 ... or 20, 10, 5, ...