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3 years ago

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Mathematics

1 answer:

blsea [12.9K]3 years ago

5 0

Answer:

a) t(n) = 8n -23

b) t(n) = 7n +24

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

d) t(n) = 1.8n +7

Step-by-step 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

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

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