How do you find the explicit formula for the following sequence 20,15,10,5,0?

Question

Lincoln Anderson · Accepted Answer

To find the explicit formula for an arithmetic sequence you must use the formula #t_n = a+ (n - 1)d#.

In the formula given above: -#t_n# is the nth term -#n# is the term's number in the sequence. -#d# is the common difference separating the terms in your sequence -#a# is the first term #t_n = 20 + (n - 1)xx -5# #t_n = 20 - 5n + 5# #t_n = 25 - 5n# This formula is now completely simplified, and as soon as you plug in a number for #n#, or a term, you can find it's term or it's number in the sequence, respectively. Example Find the 26th term in the sequence. #t_26 = 25 - 5 xx 26# #t_26 = 25 - 130# #t_26 =-105# Find which number of term has the value of #-60# in the sequence. #-60 = 25 - 5n# #-85 = -5n# #17 = n# Practice exercises: a) Find the explicit formula b) Find the 37th term c) Find the value of #n# if the term has a value of #74# Good luck!

Chloe Alexander · Answer

undefined To find the explicit formula for the sequence $20, 15, 10, 5, 0$, observe that each term decreases by 5 from the previous term.

The general form of the sequence can be expressed as $a_n = 20 - 5n$, where $a_n$ represents the $n$th term of the sequence.

Therefore, the explicit formula for the given sequence is $a_n = 20 - 5n$.

Sadie Ackerman · Answer

undefined To find the explicit formula for the sequence 20, 15, 10, 5, 0, we first need to identify the pattern or rule that governs how each term is obtained from the previous one.

Upon examining the sequence, we can see that each term is decreasing by 5 from the previous term. In other words, the nth term (where n is the position in the sequence) is given by:

$$ a_n = 20 - 5(n-1) $$

This formula represents the explicit formula for the given sequence. It calculates each term in the sequence by starting with 20 and subtracting 5 times the position of the term minus 1.