Final answer:
The nᵗʰ term of the sequence (-10, 290, 590, 890, 1190) is found to be 300n - 310, determined through the formula for the nᵗʰ term of an arithmetic sequence.
Step-by-step explanation:
To determine the nth term of the given sequence (-10, 290, 590, 890, 1190), we first need to look for a pattern in the sequence. By examining the differences between successive terms, we can observe that the series is increasing by 300 each time. This is a clear indication of an arithmetic sequence where the common difference (d) is 300. To find the nth term of an arithmetic sequence, we use the formula:
an = a1 + (n - 1) × d
Where an is the nth term, a1 is the first term, and d is the common difference. Applying this formula:
- First term (a1) = -10
- Common difference (d) = 300
- an = -10 + (n - 1)× 300
We simplify:
an = -10 + 300n - 300
an = 300n - 310
Therefore, the nth term of the given sequence is 300n - 310.