Find the nth term of this sequence
1,3,9,27,81
To find the nth term of a sequence, we need to identify the pattern in the sequence.
Looking at the given sequence: 1, 3, 9, 27, 81
We can observe that each term is obtained by multiplying the previous term by 3. This is a geometric sequence with a common ratio of 3.
So, we can write the nth term as:
Tn = a * r^(n-1)
Where:
Tn is the nth term
a is the first term
r is the common ratio
In our case:
a = 1 (first term)
r = 3 (common ratio)
Therefore, the nth term can be expressed as:
Tn = 1 * 3^(n-1)
So, the nth term of the given sequence is 1 * 3^(n-1).
To find the nth term of a sequence, we need to determine the pattern or rule governing the sequence. In this case, we observe that each term is obtained by multiplying the previous term by 3.
Let's break down the sequence to see this pattern:
1 × 3 = 3,
3 × 3 = 9,
9 × 3 = 27,
27 × 3 = 81.
So, the pattern is that each term is obtained by multiplying the previous term by 3.
To find the nth term, we can use the formula for the general term of a geometric sequence:
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 in the sequence.
In our sequence, a1 = 1 and r = 3. Plugging these values into the formula gives:
an = 1 × 3^(n-1).
Therefore, the nth term of the sequence is 1 × 3^(n-1).