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The sum of first three tems of a geometric progression is 7 and sum of their squares is 21 Find the numbers

The sum of first three tems of a geometric progression is 7 and sum of their squares is 21 Find the numbers

Grade:10

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
7 years ago
Dear Stiudent,
assume three number as a/r , a , ar.
Now according to condition,
a(1/r + 1 + r) = 7 …. (1)
and
a2(1/r2 + 1 + r2) = 21 ….. (2)

Now use the idendity,
(a+b+c)2 = a2 + b2 +c2 + 2(ab+bc+ca).
and assume a=1/r, b = 1 and c = r.
Then solve simplify it using above equations. Thanks.

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