Question

Algebra 1 Grade 9

Can anyone please help me with these arithmetic sequence question?

Use this for the next 3 questions:

Consider the arithmetic sequence 3, -10, -23, -36...

Write an equation for the nth term of the sequence.

an =


Find the 15th term in the sequence.

a15 =

Which term of the sequence is -114?

Answer 1

1.
`a_(n) =16-13n`

2. 15th term is
`a_(15) =-179`

3. 10th term is -114

Explanation:

1. The nth term of the sequence is given by the formula:

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

Here, the first term a = 3 and the common difference d = -10 - 3 = -13

So,
`a_(n) =3+(n-1)(-13)`

`a_(n) =3-13n+13`

`=16-13n`

2. To find the 15th term, put n = 15 in
`a_(n) =16-13n`

`a_(15) =16-13(15)`

`a_(15) =16-195`

= -179

Hence, the 15th term
`a_(15) =-179`

3. To find the term which is -114, put
`a_(n) =-114` in
`a_(n) =16-13n` and solve for n.

-114 = 16 - 13n

13n = 16+114

13n = 130

n = 130/13

= 10

Hence, the tenth term is -114.