bajoriay said:Homework Statement
The sum S n of the first n terms of a geometric sequence whose nth term is u n is given by
7n-an / 7n
Where a > 0
Find an expression for un
Find the first term and the common ratio of the sequence
Consider the sum to infinity of the sequence
Determine the values of a such that the sum to infinity exists
Find the sum to infinity when it exists
I tried to make it equal to the equation for Sn but it doesn't seem to be helping.
Thanks in advance
That's the right way. Pls post your working.bajoriay said:I tried to make it equal to the equation for Sn but it doesn't seem to be helping.
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant value called the common ratio. For example, in the sequence 2, 6, 18, 54, the common ratio is 3.
The formula for finding the nth term of a geometric sequence is an = a1rn-1, where an is the nth term, a1 is the first term, and r is the common ratio.
A sequence is geometric if the ratio between successive terms is constant. This means that you can divide any term by the previous term and always get the same value. For example, in the sequence 4, 8, 16, 32, the ratio between successive terms is 2.
The formula for finding the sum of a finite geometric sequence is Sn = a1(1-rn)/(1-r), where Sn is the sum of the first n terms, a1 is the first term, and r is the common ratio.
Geometric sequences can be used to model various real-life situations. For example, population growth, compound interest, and depreciation of assets can all be represented by geometric sequences. They can also be used in physics to model the motion of objects in a constant acceleration.