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Need help finding sequence rule asap, Double 12 point reward!

Need help finding sequence rule asap, Double 12 point reward!-example-1
User Zalika
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2 Answers

5 votes

Arithmetic sequences are generated by taking some initial term and continually adding or subtracting a constant term from it. What this means is that the differences between neighboring pairs of terms will always be the same - that difference gives us our constant term.


The first sequence contains the terms 17, 22, 27, 32, etc. Taking the differences of the neighboring pairs, we find that 22 - 17 = 27 - 22 = 32 - 27 = 5. If we start with 12 and add 5 once, we get 17; if we add 5 twice, we get 22, and so on. Written out in equation form:


17 = 12 + 5(1)

22 = 12 + 5(2)

27 = 12 + 5(3)


and in general,
t_n=12+5n=5n+12.


In the second sequence, we obtain each following term by subtracting 5 from the previous one, which has the same effect as adding -5. We add -5 to 19 once to get 14, twice to get 9, etc. Again, in equation form, that's


14 = 19 + (-5)(1)

9 = 19 + (-5)(2)

4 = 19 + (-5)(3)


and in general,
t_n=19 + (-5)n=-5n+19

User Eric Routhier
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8.3k points
1 vote

the easiest way is to plug and chug since you are given options



Q3

the first term is 17

plug in 1 for n and see which ones give you 17 as the result

the only one is 2nd option

answer is 2nd option or
t_n=5n+12



Q4

plug and chug

first term is 14

put 1 for n and see which one give you 14

only one is 2nd option

answer is 2nd option or
t_n=-5n+19

User Dusan Radovanovic
by
8.0k points

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