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Please help me with number 4!!

Please help me with number 4!!-example-1
User Angelic
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8.5k points

1 Answer

3 votes

Answer:

a)

Common Difference: d = 9


a_(52) = 456

Explicit:
a(n) = -12 + 9n

Explanation:

Hello!

The common difference can be found by subtracting the previous term from the next term.

Given that the sequence is
-3, 6, 15, 24...:

  • Common Difference = 6 - (-3)
    = 9

The common difference is 9.

You can see this is common throughout the whole sequence, making it arithmetic.

A geometric sequence has a common ratio, where you multiply by something to get to the next term.

An explicit equation for an arithmetic sequence is written as
a(n) = (CD)n + a(0):

  • a(n) = term value
  • n = term number (1st, 2nd, 3rd...)
  • CD = Common difference (in this case, 9)
  • a(0) = starting value

Since -3 is a(1), or the first term, we can find a(0) by subtracting 9 instead of adding.


  • -3 = a(1)

  • -12 = a(0)

We can find the equation now:
a(n) = -12 + 9n

Now that we have the equation, we can find the 52nd term by substituting 52 for n in the equation.


  • a(n) = -12 + 9n

  • a(52) = -12 + 9(52)

  • a(52) = -12 + 468

  • a(52) = 456

________________________________

Looking at your worksheet, the only thing that you may have done wrong is subtracting 9 from -3 when solving for a(0), which got you -14. In that case, you have actually subtracted by 11.

User Jpiccolo
by
8.9k points

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