Find the 54th term of the arithmetic sequence minus, 2, comma, minus, 8, comma, minus, 14, comma, point, point, .−2,−8,−14,...
Question
Find the 54th term of the arithmetic sequence
Solution
The given sequence is an arithmetic sequence, which means that each term is obtained by adding a constant difference to the previous term.
In this case, the common difference (d) is -8 - (-2) = -6.
The formula to find the nth term of an arithmetic sequence is given by:
a_n = a_1 + (n - 1) * d
where: a_n is the nth term, a_1 is the first term, n is the position of the term in the sequence, d is the common difference.
Substituting the given values into the formula, we get:
a_54 = -2 + (54 - 1) * -6 a_54 = -2 + 53 * -6 a_54 = -2 - 318 a_54 = -320
So, the 54th term of the given arithmetic sequence is -320.
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