Question

Find the twentieth term of an arithmetic
sequence where the first term is two and the common difference is $-7$

Short answer

The twentieth term of an arithmetic sequence where the first term is two and the common difference is $-7$ is $-131$

Step-by-step solution

Step 1. Given

The first term is $a_1=2$

Th common difference is $d=-7$

To find the $20th$ term of the sequence.

Step 2. Formula for nth term of the sequence.

The general term of an arithmetic sequence with first term $a_1$and the common difference $d$is

$a_n=a_1+(n-1)d$

Step 3. Substitute the values in the formula

Substitute $$\begin{gathered} a_1=2, \\ d=-7 \\ n=20 \end{gathered}$$in the formula for arithmetic sequence,

$$\begin{gathered} a_{20}=2+(20-1)(-7) \\ =2+\left(19\right)(-7) \\ =2-133 \\ =-131 \end{gathered}$$

The twentieth term is $-131$