Write a rule for the nth term of the arithmetic sequence and then find a_22 given 45,31,17,3,...

Nico Patterson

Nico Patterson

Answered question

2022-11-04

Write a rule for the nth term of the arithmetic sequence and then find a 22 given 45,31,17,3,...

Answer & Explanation

metodikkf6z

metodikkf6z

Beginner2022-11-05Added 14 answers

First, we figure out the sequence. Then we generalize it.
This one shows a decrease of 14 (-14) between every value in the series.

So, if we start with a 0 = 45 we see that a 2 = a 1 - 14 .
The next one would be a2=a1−14. Substituting our value for a 1 from the previous difference we see that:

a 2 = ( a 0 - 14 ) - 14 or a 2 = a 0 - ( 14 ) × 2

Recognizing that now our multiplier is the same as our sequence identifier (2) we can generalize the expression to:

a n = a 0 - ( 14 ) × n ; or a n = 45 - ( 14 ) × n

NOW putting in our values for a22 we can obtain:
a 22 = a 0 - ( 14 ) × 22 ; a 22 = 45 - 308 = - 263

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?