Question

Find the 50th term of the sequence 5, -2, -9, -16, ...

Answer 1

-338

Explanation:

So we have the sequence:

5, -2, -9, -16...

First, note that this is an arithmetic sequence.

This is because each individual term is the previous term added by a common difference.

We can see that this common difference is -7, because each subsequent term is 7 less than the previous one. For example, 5 minus 7 is -2, -2 minus 7 is -9, and so on.

So, to find the 50th term, we can write an explicit formula for our sequence.

The standard form for the explicit formula for an arithmetic sequence is:

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

Where a is the initial term, d is the common difference, and n is the nth term.

We can see that our initial term a is 5. And we also already determined that the common difference d is -7. So, substitute:

`x_n=5-7(n-1)`

Now, to find the 50th term, all we have to do is to substitute 50 for n. So:

`x_(50)=5-7(50-1)`

Subtract within the parentheses:

`x_(50)=5-7(49)`

Multiply:

`x_(50)=5-343`

Subtract:

`x_(50)=-338`

So, the 50th term is -338.

And we're done!