Question

What us the 20th term of the arithmetic sequence?2, -5, -12, -19,...

Answer 1

The 20th term is;

`a_(20)=-131`

Step-by-step explanation:

Given the arithemetic sequence;

`2,-5,-12,-19,\ldots`

The first term is 2;

`a=2`

The common difference d is;

`\begin{gathered} d=-5-2 \\ d=-7 \end{gathered}`

The nth term of an arithemetic sequence can be calculated using the formula;

`a_n=a+(n-1)d`

substituting for the 20th term, n=20;

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

Therefore, the 20th term is;

`a_(20)=-131`