The first term of an arithmetic sequence is equal to 200 and the common difference is equal to -10. Find the value of the 20th term.
To find the 20th term of an arithmetic sequence, we use the formula for the nth term of an arithmetic sequence:
a_n = a + (n - 1)d
where:
a is the first term of the sequence,
d is the common difference,
n is the term number, and
a_n is the nth term.
Here:
a = 200 (first term),
d = -10 (common difference),
n = 20 (we need to find the 20th term).
Substituting the values into the formula:
a_20 = 200 + (20 - 1)(-10)
Simplify the expression step by step:
Compute (20 - 1): a_20 = 200 + 19(-10)
Multiply 19 by -10: a_20 = 200 - 190
Subtract 190 from 200: a_20 = 10
Thus, the 20th term of the arithmetic sequence is 10.
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