find the 93rd term of the arithmetic sequence -5, -15, -25,...

Explanation:

Step1: Find the common difference

The common difference (d) of an arithmetic sequence is (a_{n + 1}-a_{n}). For the sequence (-5,-15,-25,\cdots), (d=-15-\left(-5\right)=-10)

Step2: Use the formula for the (n)th term of an arithmetic sequence

The formula for the (n)th term of an arithmetic sequence is (a_{n}=a_{1}+(n - 1)d), where (a_{1}) is the first term, (n) is the term number, and (d) is the common difference. Here, (a_{1}=-5), (n = 93), and (d=-10)

Substitute the values into the formula: [ \begin{align*} a_{93}&=-5+(93 - 1)\times(-10)\ &=-5+92\times(-10)\ &=-5-920\ &=-925 \end{align*} ]

Answer:

(-925)