Write a rule for the nth term of the arithmetic sequence given a_10=8, a_16=32

kadirsmr9d

kadirsmr9d

Answered question

2022-09-10

Write a rule for the nth term of the arithmetic sequence given a 10 = 8 , a 16 = 32

Answer & Explanation

illpnthr21vw

illpnthr21vw

Beginner2022-09-11Added 17 answers

For an arithmetic sequence < a 0 , a 1 , a 2 , a 3 , ... >
terms are related by the formula:
XXX a m = a n + ( m - n ) k for some constant k

In this example:
XXX a 16 = a 10 + ( 16 - 10 ) k
or (using the given values)
XXX 32 = 8 + 6 k

XX k = 4

And the initial value, a 0 is
XXX a 0 = a 10 + ( 0 - 10 ) k
or
XXX a 0 = 8 + ( - 10 ) ( 4 ) = - 32

If your standard is to use a1 as an initial value:
XXX a 1 = a 10 + ( 1 - 10 ) k
XXXXX = 8 + ( - 9 ) ( 4 ) = - 28

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