194k views
2 votes
Find the 50th term of the sequence 5, -2, -9, -16, ...

1 Answer

7 votes

Answer:

-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!

User Ashlocke
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories