MyQuestionIcon

3

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Sum of n Terms

In a G.P., th...

Question

In a G.P., the ratio between the sum of first three terms and that of the first six terms is 125 : 152.

Find its common ratio.

Open in App

Solution

$L e t space apostrophe a apostrophe space b e space f i r s t space t e r m space a n d space apostrophe r apostrophe space c o m m o n space r a t i o space o f space G. P S â�� space divided by space S â�� space equals space 125 over 152 space fraction numerator a space left parenthesis space r Â³ space minus space 1 space right parenthesis over denominator space left parenthesis space r space minus space 1 space right parenthesis end fraction space space divided by space fraction numerator a space left parenthesis space r space â�¶ space minus space 1 right parenthesis over denominator left parenthesis space r minus space 1 right parenthesis end fraction equals space fraction numerator 125 over denominator space 152 space end fraction fraction numerator left parenthesis space r Â³ space minus space 1 space right parenthesis over denominator left parenthesis space r space â�¶ space minus space 1 space right parenthesis space end fraction space space equals space fraction numerator 125 over denominator space 152 end fraction space fraction numerator left square bracket space r Â³ space minus space 1 space right square bracket over denominator left square bracket space left parenthesis r Â³ right parenthesis space Â² space minus space left parenthesis 1 right parenthesis Â² space right square bracket space end fraction space equals fraction numerator space 125 over denominator space 152 end fraction space fraction numerator left square bracket space r Â³ space minus space 1 space right square bracket over denominator space left square bracket space left parenthesis space r Â³ space minus space 1 right parenthesis space left parenthesis r Â³ space plus space 1 space right parenthesis space end fraction space equals space fraction numerator 125 over denominator 152 space end fraction space fraction numerator 1 over denominator space left square bracket space r Â³ space plus space 1 space right square bracket end fraction space space equals space fraction numerator 125 over denominator 152 space space end fraction space 152 space equals space 125 space left square bracket space r Â³ space plus space 1 space right square bracket space 152 space equals 125 space r Â³ space plus space 125 space 27 over 125 space space space equals space r space Â³ space space open parentheses 3 over 5 close parentheses Â³ space equals space r space Â³ space r equals space 3 over 5$
Common difference is

Suggest Corrections

thumbs-up

1

Similar questions

Q. 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 the

G . P

.

Q. If the ratio of the sum of first three terms and the sum first six terms of a

G . P .

125 : 152

, then the common ratio is:

Q. The ratio of the sum of first three terms is to that of first 6 terms of a G.P. is 125 : 152. Find the common ratio.

Q. If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 125 : 152, then the common ratio r is

Q. The sum of first three terms of a G.P. is to the sum of the first six terms as 125:152. Find the value of 5 times of common ratio of the G.P.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Sum of n Terms

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon