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

  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

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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

This is very simple. So you use two formulas:

Rectangle: Length • Width

Semicircle: Area =

With that, you do 0.8 ÷ 2 = 0.4 because we will be using radius. When solved, you get 0.2512... But for this problem, I will be rounding everything to the nearest hundredths.

Area of semicircle: ≈ 0.25

Now we solve for the rectangle. That is very easy. Just multiply 0.75 • 0.8 and you get 0.6

For this problem, I'm not sure why they make you round to the nearest centimeter, but if you do, you get 1 cm. Otherwise,

Round to nearest tenth: 0.9

Round to nearest hundredths: 0.85