Question

Find the 75th term of the arithmetic sequence minus, 21, comma, minus, 10, comma, 1, comma, point, point, .−21,−10,1,...

Answer 1

what is the answer

Answer 2

We notice that in this arithmetic sequence, each term is 11 more than the previous term. We want to find the 75th term of the sequence, so we start with the first term, $-21,$ and keep adding 11 until we reach the 75th term. We can use the formula for the nth term of an arithmetic sequence, $a_n=a_1+(n-1)d,$ where $a_n$ is the nth term, $a_1$ is the first term, $n$ is the number of terms, and $d$ is the common difference. In this case, $a_1=-21,$ $n=75,$ and $d=11$, so we plug these values into the formula: \begin{align*}
a_n&=-21+(75-1)11 \\
&=-21+(74)(11) \\
&=-21+814 \\
&=\boxed{793}.
\end{align*}

Answer 3

The 75th term of the given arithmetic sequence is 793.