Did you know?
In an exponential sequence, each term is obtained by multiplying the previous term by a constant called the common ratio.
For example, given that the 5th term of an exponential sequence is greater than the 4th term by 131/2 and the 4th term is greater than the 3rd term by 9, we can find the first term and common ratio.
To solve this problem, we can set up an equation using the information provided. Let's denote the first term as 'a' and the common ratio as 'r'.
From the given information, we have:
4th term = a * r^3
5th term = a * r^4
According to the problem, the 5th term is greater than the 4th term by 131/2. Therefore, we can set up the following equation:
a * r^4 - a * r^3 = 131/2
Similarly, the 4th term is greater than the 3rd term by 9:
a * r^3 - a * r^2 = 9
By solving these two equations, we can find the values of 'a' and 'r', which will give us the first term and common ratio of the exponential sequence in question.
