Question

Any
• The sum of first three terms of a G.P is to the sum of the first six terms as 125:152 find the common ratio of G.P
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Answer 1

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Given:

Sum of first three terms of GP is to the sum of first six terms as 125:152

To find:

Common ratio of GP = ?

Solution:

Refer attachment

Formulas used:

1. Sum of nth term of GP Formula

$\\ Sn = \dfrac{a(r {}^{n} - 1)}{r - 1} \\ a \: \: is \: the \: first \: term \: and \: r \: is \: the \: \\ common \: ratio \: and \: n \: is \: terms \: \\ in \: number$

2) .$\\ \\ a {}^{2} - b {}^{2} = (a + b)( a - b)$

3. Cube root of 27 is 3 and of 125 is 5

Required Answer:

$\\ Therefore \: the \: common \: ratio \: (r) \\ = \: \: \dfrac{3}{5}$

Basic point:

# If we inverse ratio of left hand side at the same time inverse ratio of right hand side

# Cancel the similar terms in ratio

#Solve more such questions to get a good hold on it