$$ \begin{aligned} a_{n} & =a_{1}+(n-1) d & & \text { General Formula for Arithmetics } \ & =13+(n-1)(-5) & & a_{1}=13 \text { and } d=-5 \ & =13+(-5) n+50 & & \text { Distributive Property } \ & =-5 n+180 & & \text { Simplify. } \end{aligned} $$ Reset Part B Find the 20th term In the sequence. $$ \square $$

Question

UpStudy AI · Accepted Answer

To find the 20th term of the arithmetic sequence, let's follow the steps using the provided information.

### Given:
- **First term ($$a_1$$)**: 13
- **Common difference ($$d$$)**: -5

### Formula for the $$n$$th term of an arithmetic sequence:
$$
a_n = a_1 + (n - 1) \cdot d
$$

### Calculating the 20th term ($$a_{20}$$):
$$
\begin{aligned}
a_{20} &= a_1 + (20 - 1) \cdot d \
&= 13 + 19 \cdot (-5) \
&= 13 - 95 \
&= -82
\end{aligned}
$$

### **Answer:**
The 20th term in the sequence is **$$-82$$**.
The 20th term in the sequence is -82.

Reset
Part B

Find the 20th term In the sequence.

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