Given the geometric sequence: 26, 2617, 26289, ⋯
Find an explicit formula for an, where the first term is a1=26.
an=
Find a6=
please help out
To find the explicit formula for the given geometric sequence, we need to determine the common ratio (r). The common ratio can be found by dividing any term in the sequence by its previous term. Let's use the second and first terms:
r = term2 / term1 = 2617 / 26 = 101
So, the common ratio (r) is 101.
The explicit formula for a geometric sequence is given by:
an = a1 * r^(n-1)
Where:
an represents the nth term,
a1 represents the first term, and
r represents the common ratio.
Now, we can substitute the given values to find the explicit formula:
an = 26 * 101^(n-1)
To find a specific term, such as a6, we can substitute n with the corresponding value:
a6 = 26 * 101^(6-1)
= 26 * 101^5
= 26 * 10,201,010,101
= 265,277,263,326
Therefore, the explicit formula for an in this geometric sequence is an = 26 * 101^(n-1), and a6 is equal to 265,277,263,326.