Write a rule for the sequence
4, 8, 16, 32, …
Each term is obtained by multiplying the previous term by 2.
geometric sequence
Tn = a r^(n-1)
Tn = 4 * 2^(n-1)
Correct! This is the formula for the nth term of a geometric sequence where the first term is a and the common ratio is r. In this case, a = 4 and r = 2.
To write a rule for the given sequence 4, 8, 16, 32, ..., we can observe that each term is obtained by multiplying the previous term by 2.
So, if we denote the first term as a₁, the second term as a₂, and so on, we can write the rule as:
aₙ = aₙ₋₁ * 2,
where aₙ represents the nth term and aₙ₋₁ represents the (n-1)th term in the sequence.
Using this rule, we can find any term in the sequence by multiplying the previous term by 2. For example, to find the 5th term, we just need to multiply the 4th term (32) by 2:
a₅ = 32 * 2 = 64.
Therefore, the 5th term in the sequence is 64.