Find the general term of the geometric sequence
36 , 6 , 1 , 1/6 , 1/36 ,... .
Each number is divided by 6.
To find the general term of a geometric sequence, we need to identify the common ratio (r) first. In this case, to move from one term to the next, we are dividing by 6. So the common ratio is 1/6.
The first term (a₁) is given as 36.
Now that we have the common ratio and the first term, we can use the formula for the general term of a geometric sequence, which is:
aₙ = a₁ * r^(n-1)
where 'aₙ' represents the nth term of the sequence, 'a₁' is the first term, 'r' is the common ratio, and 'n' is the position of the term we want to find.
In this case, we want to find the general term, so we'll let 'n' be a variable. The general term of this sequence is:
aₙ = 36 * (1/6)^(n-1)
Therefore, the general term of the geometric sequence is 36 * (1/6)^(n-1).