Hi! I need help with this question. Thank you!
Directions: Write the expression for the nth term of the following geometric sequence.
5, 10, 20, 40, ...
10 = 2 * 5
20 = 2 * 10
40 = 2 * 20
I geometric sequence :
an = a1 * r ^ ( n - 1 )
where a1 is the first term of the sequence.
r is the common ratio.
n is the number of the term to find
In this case :
a1 = 5
r = 2
an = a1 * r ^ ( n - 1 )
an = 5 * 2 ^ ( n - 1 )
Hello! I'd be happy to help you with that question.
To find the nth term of a geometric sequence, you need to determine the common ratio (r) and the first term (a₁) of the sequence.
In this case, we can see that the common ratio is 2 because each term is twice the previous term (10 ÷ 5 = 2, 20 ÷ 10 = 2, and so on). The first term, a₁, is 5.
The formula to find the nth term of a geometric sequence is:
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.
Now, let's use the formula to find the expression for the nth term of the given geometric sequence.
For this sequence, a₁ is 5, and r is 2. Plugging these values into the formula, we get:
an = 5 * 2^(n-1).
Therefore, the expression for the nth term of the given geometric sequence is 5 * 2^(n-1).
I hope this explanation helps! If you have any more questions, feel free to ask.