this is a difficult question for me please help! thankyou

A sequence is defined recursively by
an + 1 = 3an − n, a1 = 2.
Find the first six terms of the sequence.
a1 =
a2 =
a3 =
a4 =
a5 =
a6 =

Oh, recursive sequences, they can be quite tricky! Let me see if I can make it a bit more fun for you.

Let's solve this one step at a time, like following a trail of breadcrumbs... that leads to math answers!

Starting with a1 = 2, we need to find the next term, a2. We can use the recursive formula to get there:

a2 = 3a1 - 1

Now, substituting the value of a1, we get:

a2 = 3(2) - 1

That gives us a2 = 6 - 1, which simplifies to a2 = 5.

On to the next term!

a3 = 3a2 - 2. Using a2 = 5, we can substitute it in:

a3 = 3(5) - 2

That gives us a3 = 15 - 2, which simplifies to a3 = 13.

Let's keep going!

a4 = 3a3 - 3. Substituting a3 = 13:

a4 = 3(13) - 3

That gives us a4 = 39 - 3, which simplifies to a4 = 36.

Now for the fifth term!

a5 = 3a4 - 4. Substituting a4 = 36:

a5 = 3(36) - 4

That gives us a5 = 108 - 4, which simplifies to a5 = 104.

And finally, the sixth term!

a6 = 3a5 - 5. Substituting a5 = 104:

a6 = 3(104) - 5

That gives us a6 = 312 - 5, which simplifies to a6 = 307.

So, the first six terms of the sequence are:
a1 = 2
a2 = 5
a3 = 13
a4 = 36
a5 = 104
a6 = 307

I hope that helped brighten up the math for you!

To find the first six terms of the sequence, we'll use the recursive formula provided.

1. Start with the initial term a1 = 2.

a1 = 2

2. Use the recursive formula to find the next term.

a2 = 3a1 - 1 = 3(2) - 1 = 5

3. Repeat step 2 to find the subsequent terms.

a3 = 3a2 - 2 = 3(5) - 2 = 13
a4 = 3a3 - 3 = 3(13) - 3 = 36
a5 = 3a4 - 4 = 3(36) - 4 = 104
a6 = 3a5 - 5 = 3(104) - 5 = 311

Therefore, the first six terms of the sequence are:
a1 = 2
a2 = 5
a3 = 13
a4 = 36
a5 = 104
a6 = 311

Sure, I can help you with that!

To find the first six terms of the sequence, we can use the given recursive formula:

an + 1 = 3an − n

Starting with a1 = 2, we can plug in the values into the formula to find the next terms.

Step 1: Find a2
Plug in n = 1 (since it's the first term) into the formula:
a2 = 3a1 - 1
= 3(2) - 1
= 6 - 1
= 5
Therefore, the second term is a2 = 5.

Step 2: Find a3
Plug in n = 2:
a3 = 3a2 - 2
= 3(5) - 2
= 15 - 2
= 13
So, the third term is a3 = 13.

Step 3: Find a4
Plug in n = 3:
a4 = 3a3 - 3
= 3(13) - 3
= 39 - 3
= 36
Hence, the fourth term is a4 = 36.

Step 4: Find a5
Plug in n = 4:
a5 = 3a4 - 4
= 3(36) - 4
= 108 - 4
= 104
Therefore, the fifth term is a5 = 104.

Step 5: Find a6
Plug in n = 5:
a6 = 3a5 - 5
= 3(104) - 5
= 312 - 5
= 307
Thus, the sixth term is a6 = 307.

To summarize, the first six terms of the sequence are as follows:
a1 = 2
a2 = 5
a3 = 13
a4 = 36
a5 = 104
a6 = 307

a1 = 2

a2 = 3a1-1 = 3*2-1 = 5
a3 = 3a2-1 = 3*5-1 = 14
and so on