The first term of a geometric sequence is 3 and the common ratio of the sequence is 1/4 .
Write down a formula for the nth term of the sequence.
For ANY geometric sequence,
a_n = ar^(n-1)
so plug in your numbers
Sure! To find the nth term of a geometric sequence, you can use the formula:
aₙ = a₁ * (r)^(n-1),
where aₙ represents the nth term, a₁ is the first term, r is the common ratio, and n is the position of the term you want to find.
So, plugging in the given values, the formula for the nth term of your sequence would be:
aₙ = 3 * (1/4)^(n-1).
Now that we have the formula, we can calculate all the terms of the sequence, and watch as it geometrically adds up! Just try not to get too dizzy from all the numbers spinning around.
To find the formula for the nth term of a geometric sequence, we can use the formula:
aₙ = a₁ * r^(n-1)
where:
aₙ represents the nth term of the sequence,
a₁ is the first term of the sequence,
r is the common ratio of the sequence,
n is the position of the term we want to find.
Given that the first term, a₁, is 3 and the common ratio, r, is 1/4, we can substitute these values into the formula:
aₙ = 3 * (1/4)^(n-1)
So, the formula for the nth term of the sequence is aₙ = 3 * (1/4)^(n-1).
To find the formula for the nth term of a geometric sequence, we can use the general formula:
an = a1 * r^(n-1)
Where:
- an represents the nth term of the sequence
- a1 represents the first term of the sequence
- r represents the common ratio of the sequence
- n represents the position of the term in the sequence
In this case, the first term (a1) is given as 3, and the common ratio (r) is given as 1/4. Plugging these values into the formula, we get:
an = 3 * (1/4)^(n-1)