Find the first 5 terms of the arithemitic sequence whose seventh term is 22 and whose eleventh term is 6.

The first 5 terms of the arithemitic sequence are 46, 42, 38, 34 and 30.

Step-by-step explanation:

Given that:

The arithemitic sequence whose seventh term is 22 and whose eleventh term is 6.

To Find:

The first 5 terms of the arithemitic sequence.

We know that:

aₙ = a + (n - 1)d

Where,

aₙ = nth term a = First term n = Number of termsd = Common difference

We have:

Seventh term = 22

⟶ a + (7 - 1)d = 22

⟶ a + 6d = 22

⟶ a = 22 - 6d

Evelenth term = 6

⟶ a + (11 - 1)d = 6

⟶ a + 10d = 6

Substituting the value of a.

⟶ 22 - 6d + 10d = 6

⟶ 22 + 4d = 6

⟶ 4d = 6 - 22

⟶ 4d = - 16

⟶ d = - 16/4

⟶ d = - 4

In equation (i).

⟶ a = 22 - 6d

Putting the value of d.

⟶ a = 22 - 6(- 4)

⟶ a = 22 + 24

⟶ a = 46

Now we have to find the first 5 terms:

a = 46a + d = 46 + (- 4) = 46 - 4 = 42a + 2d = 46 + 2(- 4) = 46 - 8 = 38a + 3d = 46 + 3(- 4) = 46 - 12 = 34a + 4d = 46 + 4(- 4) = 46 - 16 = 30

Hence,

The first 5 terms of the arithemitic sequence are 46, 42, 38, 34 and 30.

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a.this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b.this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )