Question

Hello,can you please help me with question 25 in the photo?Thank you

Answer 1

Given:

The arithmetic sequence:

`7,3,-1,-5,...`

Required:

We need to find the nth term equation and value of 20 th term.

Step-by-step explanation:

The first term of the given arithmetic sequence is a =7.

`d=3-7=-4`

The common difference is d =-4.

Consider the nth term formula for the arithmetic sequence.

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

Substitute a =7 and d =-4 in the formula.

`a_n=7+(n-1)(-4)`

`a_n=7+n(-4)-1(-4)`

`a_n=7-4n+4`

`a_n=11-4n`

The equation for the nth term of the given sequence is

`a_n=11-4n.`

Substitute n=20 in the equation to find the value of 20 th term.

`a_(20)=11-4(20)`

`a_(20)=11-80`

`a_(20)=-69`

Final answer:

`a_n=11-4n`

`a_(20)=-69`