Question

The sum of G.P. is 765. If its lst term is 3 and last term is 384. find the common ratio.

Answer 1

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Answer 2

Given:

The sum of G.P. is 765. If its first term is 3 and last term is 384.

To Find:

find the common ratio.

Step-by-step explanation:

• As first term is $3$. So, $a_{1}=3$.
• The last term is
• $a_{n}=a\times r^{n-1} =384\\3\times r^{n-1} =384\\r^{n-1} =128\\r^{n} =128\times r$

• The sum of terms is $765$

$S_{n}=a(r^{n}-1 ) \div (r-1)\\765=3(r^{n}-1 ) \div (r-1)\\255=(r^{n}-1 ) \div (r-1)$

• Now using the value obtained in previous step and substituting it in the sum equation we get

$255\times r -255= 128\times r -1\\127\times r = 254\\r=2$

The common ratio is 2