Find the nth term of the geometric sequence whose initial term is 7 and common ration is 7. (your answer must be a function of n)
For a GS,
termn = a(r)^(n-1)
so termn = 7(7)^(n-1)
= 7^n
To find the nth term of a geometric sequence, we can use the formula:
nth term = a * r^(n-1)
where:
- nth term is the desired term of the sequence
- a is the initial term
- r is the common ratio
- n is the position of the term in the sequence
Given that the initial term (a) is 7 and the common ratio (r) is also 7, we can substitute these values into the formula:
nth term = 7 * 7^(n-1)
So, the nth term of the geometric sequence is given by the function: f(n) = 7 * 7^(n-1)
To find the nth term of a geometric sequence, we can use the formula:
an = a1 * r^(n-1)
where an is the nth term, a1 is the initial term, r is the common ratio, and n is the position of the term in the sequence.
In this case, the initial term (a1) is 7 and the common ratio (r) is also 7.
Therefore, the nth term of the geometric sequence is:
an = 7 * 7^(n-1)
So, the answer is:
an = 7 * 7^(n-1)