The sum of the first 3 terms of a geometric series is 26. The sum of the first 6 terms is 728. Find the first term and common ratio.
Question
Solution 1
Let's denote the first term of the geometric series as 'a' and the common ratio as 'r'.
From the problem, we know that:
a + ar + ar^2 = 26 (This is the sum of the first 3 terms)
a + ar + ar^2 + ar^3 + ar^4 + ar^5 = 728 (This is the sum of the first 6 terms)
We can simplify the second equa Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv
Similar Questions
The sum of the first 3 terms of a geometric series is 26. The sum of the first 6 terms is 728. Find the first term and common ratio.
Find the sum of the infinite geometric series, with first term 1 and common ratio 1/2Choices:- -2 2 0 -1
In a geometric progression, the sum of the first n terms is 3069 and the first term is 3. If the nth term in the progression is 1536, find the common ratio
The sum of the first n terms of the geometric progression, whose first term is 4 and the common ratio is 3, is 4372. Find na.7b.8c.6d.9
The sum of a geometric series is 3. The series of squares of its terms has sum 18. Findseries.