Final answer:
The nᵗʰ term of the sequence is found by identifying the pattern of differences between terms and creating a formula. For this sequence, the nᵗʰ term is an = 33 - 30n.
Step-by-step explanation:
The student is looking for the nᵗʰ term of a sequence. Given the sequence 3, -27, -57, -87, -117, we need to determine a pattern to create a formula for the nᵗʰ term. By observing the differences between the terms, we see that each term decreases by 30. The first term, a1, is 3. So, the difference from the first term to the nth term can be expressed as (n-1) times the common difference, which is -30.
Therefore, the nᵗʰ term will be an = a1 + (n-1)d = 3 + (n-1)(-30) = 3 - 30n + 30 = 33 - 30n. So, the formula for the nᵗʰ term of the sequence is an = 33 - 30n.
Observing the sequence, it seems that each term is decreasing by 30.
To find the ��ℎn th term of this sequence, we can use the formula for an arithmetic sequence:
nth term=�+(�−1)×�
nth term=a+(n−1)×d
Where:
�a is the first term of the sequence (in this case, �=3a=3)�n is the term number you want to find�d is the common difference between consecutive terms (here, �=−30d=−30)Let's determine the ��ℎ nth term of this sequence. If you're looking for a specific term, say the 10th term
nth term=3+(10−1)×(−30)
nth term=3+(10−1)×(−30)
nth term=3+9×(−30)
nth term=3+9×(−30)
nth term=3−270
nth term=3−270
nth term=−267
nth term=−267
Therefore, the 10th term of this sequence is -267. You can use this formula to find any term in this sequence by substituting the appropriate value for
�
n.