Write an equation for the $n$n th term of the arithmetic sequence. Then find $a_{30}$a30 .$6,\ 12,\ 18,\ 24,\ ...$6, 12, 18, 24, ...$a_n=$an= $a_{30}=$a30=
Question
Write an equation for the n th term of the arithmetic sequence. Then find a30 .6, 12, 18, 24, ...an= a30=
Solution
The nth term of an arithmetic sequence can be found using the formula:
a_n = a_1 + (n - 1) * d
where: a_n is the nth term a_1 is the first term d is the common difference
In this sequence, the first term a_1 is 6 and the common difference d is 6 (12 - 6 = 6).
So, the nth term of the sequence is:
a_n = 6 + (n - 1) * 6 a_n = 6n
To find the 30th term a_30, substitute n = 30 into the equation:
a_30 = 6 * 30 a_30 = 180
So, the 30th term of the sequence is 180.
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