Question

Need help on 15 and 16 PLEASEE!!!

Answer 1

Part 15) The next three terms are 5/8,3/4 and 7/8

Part 16) The 37th term is -35.5

Explanation:

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant and this constant is called the common difference (d)

Part 15) Find the next three terms of the arithmetic sequence

`(1)/(8),(1)/(4),(3)/(8),(1)/(2),...`

so

`a1=1/8\\ a2=1/4\\ a3=3/8\\ a4=1/2\\ a2-a1=1/4-1/8=1/8\\ a3-a2=3/8-1/4=1/8\\ a4=a3=1/2-3/8=1/8`

The common difference is equal to

d=1/8

Find the next three terms of the arithmetic sequence

Find a5

`a5=a4+d` ----->
`a5=1/2+1/8=5/8`

Find a6

`a6=a5+d` ----->
`a6=5/8+1/8=3/4`

Find a7

`a7=a6+d` ----->
`a7=3/4+1/8=7/8`

therefore

The next three terms are

5/8,3/4 and 7/8

Part 16) what is the 37th term of the arithmetic sequence

`4.1,3,1.9,0.8,...?`

so

`a1=4.1\\ a2=3\\ a3=1.9\\ a4=0.8`

`a2-a1=3-4.1=-1.1\\ a3-a2=1.9-3=-1.1\\ a4=a3=0.8-1.9=-1.1`

The common difference is equal to

d=-1.1

We can write an Arithmetic Sequence as a rule

`an=a1+d(n-1)`

substitute the values

`an=4.1-1.1(n-1)`

For n=37

substitute

`a37=4.1-1.1(37-1)`

`a37=4.1-1.1(36)`

`a37=-35.5`