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NO LINKS!!!

4. Given a term in the sequence and the common difference (d), write the equation of the sequence in the form t(n) = mn + b. Part 1

a. t(34)= 249, difference = 8

b. t(36)= 276, difference = 7

c. t(40) = -1191, difference= -30

d. t(12)= 28.6, difference= 1.8

User Bentaye
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1 Answer

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20 votes

Answer:

a) t(n) = 8n -23

b) t(n) = 7n +24

c) t(n) = -30n +9

d) t(n) = 1.8n +7

Explanation:

The general equation for the n-th term of an arithmetic sequence is ...

an = a1 +d(n -1)

Expanding this, we find ....

an = a1 +d·n -d = d·n +(a1 -d)

Comparing that to the form ...

an = m·n +b

we see that ...

m = d

b = (a1 -d)

If you're given a term other than a1, say ak, then you have ...

ak = d·k +(a1 -d)

(a1 -d) = ak -d·k

For a given term and common difference, we can write the desired equation as ...

t(n) = d·n +(ak -d·k) . . . . . . given t(k) = ak and d

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Once again, it is convenient to use a spreadsheet to do the calculations for a number of different instances of this problem.

a) t(n) = 8n -23

b) t(n) = 7n +24

c) t(n) = -30n +9

d) t(n) = 1.8n +7

NO LINKS!!! 4. Given a term in the sequence and the common difference (d), write the-example-1
User Vahid Ghadiri
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