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Answer:
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.
