Determine if each of the following sequences is arithmetic. If so, write Zrecursive rule and an explicit rule for the sequence. If not, explain why. (Lesson 4.2) 3. -8,-1, 6, 13... 4. 1, 8, 27,81...

9514 1404 393

  3. yes: a[1] = -8, a[n] = a[n-1] +7; an = -8 +7(n -1)

  4. no (no common difference)

Step-by-step explanation:

An arithmetic sequence is one in which each term has the same difference from the term before it.

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3. -1 -(-8) = 7; 6 -(-1) = 7; 13 -6 - 7. The differences are all 7, so the terms have a common difference. This sequence is arithmetic.

The general form of the recursive rule for an arithmetic sequence with first term a1 and common difference d is ...

  a[1] = a1; a[n] = a[n-1] +d . . . . . recursive rule

  a[1] = -8; a[n] = a[n-1] +7

The general form of the explicit rule for an arithmetic sequence is ...

  an = a1 +d(n -1)

  an = -8 +7(n -1)

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4. The differences are ...

  8 -1 = 7; 27 -8 = 19; 81 -27 = 54 . . . the differences are not common

This sequences is not arithmetic.

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