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Write a recursive rule and an explicit rule for the arithmetic sequence 19,9,-1,-11,...

User Yossile
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1 Answer

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the formula is an =a1+d(n-1)

where a1 is the first terms

d is the common difference

a1= 19

d 1= 9-19 = -10

check: -1-9 = -10 the sequence goes down by 10

n is the term number


an = 19 - 10(n-1)

we can distribute

an = 19 -10n +10

an = 29-10n


Check our work:

a4 = 29 - 10*4

= 29 - 40

= -11

the 4th term is -11 which 19,9,-1,-11,... shows, so we are good


Answer: an = 19 - 10(n-1) or an = 29-10n

User Bruin
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