Find the 12th term of the arithmetic sequence 20, 14, 8, 2, -4

listgrein6u

listgrein6u

Answered question

2022-09-10

Find the 12th term of the arithmetic sequence 20, 14, 8, 2, -4

Answer & Explanation

Nelson Santana

Nelson Santana

Beginner2022-09-11Added 13 answers

A term of an arithmetic sequence can be calculated with the formula:

t n = a + ( n - 1 ) d

where:
t n = =any term in the arithmetic sequence
a= first term
n= term number/number of terms
d= common difference

To find the 12 t h term of the sequence, we first need to find d, the common difference. We can do this by subtracting t 1 from t 2 :

t 2 - t 1
=14−20
=−6

Now that you have the common difference, substitute all your known values into the formula to solve for t 12 :

t n = a + ( n - 1 ) d
t 12 = 20 + ( 12 - 1 ) ( - 6 )
t 12 = 20 + ( 11 ) ( - 6 )
t 12 = 20 - 66
t 12 = - 46

so the 12 t h term is −46.

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