Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, $a_{1}$, and common difference, $d$. Find $a_{150}$ when $a_{1}=-40, d=5$
Answer
\(\boxed{705}\) is the 150th term of the sequence.
Step 1 ：Given the first term, $a_{1}=-40$, and common difference, $d=5$, of an arithmetic sequence, we are to find the 150th term, $a_{150}$.
Step 2 ：We use the formula for the nth term of an arithmetic sequence, which is $a_{n} = a_{1} + (n-1)d$.
Step 3 ：Substitute the given values into this formula: $a_{150} = -40 + (150-1)\times5$.
Step 4 ：Simplify the expression to get $a_{150} = -40 + 149\times5$.
Step 5 ：Calculate the result to get $a_{150} = 705$.
Step 6 ：\(\boxed{705}\) is the 150th term of the sequence.
