Final answer:
The general term for the sequence -10, -20, -30, -40, -50,... is ann = -10n, where n is the position of the term in the sequence.
Step-by-step explanation:
To find the general term of the given sequence, we can use the pattern that it presents. The sequence is -10, -20, -30, -40, -50,.... We notice that each term is decreasing by 10 from the previous one.
The sequence is an arithmetic sequence where the first term (a1) is -10 and the common difference (d) is -10.
The general term of an arithmetic sequence is given by the formula an = a1 + (n - 1) × d. Substituting the values from our sequence into this formula gives us:
an = -10 + (n - 1) × (-10)
This simplifies to:
an = -10 - 10(n - 1)
Or:
an = -10n (since -10 × -1 is +10, canceling out the initial -10)
Therefore, the general term for the given sequence is an = -10n.