1. Write a rule for the sequence
3,-3,-9,-15,...
The rule is adding -6
Thank you!
Your welcome! :)
To write a rule for the sequence 3, -3, -9, -15, we need to identify the pattern or relationship between the terms.
Looking at the sequence, we can observe that each term is obtained by subtracting 6 from the previous term. This means that to generate the next term in the sequence, we need to subtract 6 from the current term.
Based on this pattern, we can write the recursive rule for the sequence as follows:
aₙ = aₙ₋₁ - 6,
where aₙ represents the nth term in the sequence and aₙ₋₁ represents the (n-1)th term.
Using this recursive rule, we can find any term in the sequence by starting with the first term (a₁ = 3) and applying the rule repeatedly to obtain subsequent terms.
For example, to find the 5th term in the sequence, we can apply the rule four times:
a₁ = 3
a₂ = a₁ - 6 = 3 - 6 = -3
a₃ = a₂ - 6 = -3 - 6 = -9
a₄ = a₃ - 6 = -9 - 6 = -15
a₅ = a₄ - 6 = -15 - 6 = -21
Therefore, the 5th term in the sequence is -21.
By repeating this process, we can generate any term in the sequence by applying the rule to the previous term.