Question

Please help me with number 4!!

Answer 1

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`

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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.