Final answer:
The nth term of the given arithmetic sequence -4, -2.6, -1.2, 0.2, 1.6 is 1.4n - 5.4, where n is the position in the sequence.
Step-by-step explanation:
The given sequence is -4, -2.6, -1.2, 0.2, 1.6. To find the n terms, we must identify the pattern of the sequence. We can see that each term is increasing by 1.4:
-4 to -2.6 is an increase of 1.4 (-4 + 1.4 = -2.6)
-2.6 to -1.2 is an increase of 1.4 (-2.6 + 1.4 = -1.2)
-1.2 to 0.2 is an increase of 1.4 (-1.2 + 1.4 = 0.2)
0.2 to 1.6 is an increase of 1.4 (0.2 + 1.4 = 1.6)
To find the nth term, we start with the first term and add the common difference multiplied by (n-1), where n is the position in the sequence.
The nth term formula for this arithmetic sequence is:
an = a1 + (n - 1)d
Where a1 is the first term and d is the common difference.
an = -4 + (n - 1)(1.4)
Simplified:
an = -4 + 1.4n - 1.4
an = 1.4n - 5.4
So, the nth term of the sequence is 1.4n - 5.4.