Question

if each term of an infinite G. P is three times the sum of the succeeding terms and sum of first two terms is 15,find the sum of its infinite terms​

Answer 1

Answer:

yrbsybryjrju6hhrmrmfm

Answer 2

Step-by-step explanation:

If you multiply a geometric progression by its common ratio, you get the same progression again, but without the first term.

If the first term is three times the sum of all the remaining terms, that means that the sum of all the terms is four times the sum of those terms starting from the second term.

Putting these two ideas together, if “SUM” is the sum of all the terms, then SUM is four times the common ratio multiplied by SUM.

Hence the common ratio is 1/4.

We are also told that the first two terms add to 20. If the first term is “F”, the second term is F/4, and for their sum to be 20 we’d need F = 16.

Conclusion: The series in question is 16 + 4 + 1 + 1/4 + 1/16 + ….