Answer:
an = 7n -5
Step-by-step explanation:
The sequence is increasing, so the coefficient of n will be positive. Try n=1 in the two rules matching this and see which works:
2 ≠ 7·1 +2 . . . . . doesn't work, because 2 ≠ 9
2 = 7·1 -5 . . . . . the 2nd choice matches the given sequence
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Alternate solution
The general term for an arithmetic sequence with first term a1 and common difference d is ...
an = a1 + d(n -1)
Here, the first term is 2 and the common difference is 7, so the general term is ...
an = 2 + 7(n -1)
This can be simplified to the form that the answers have:
an = 2 +7n -7 . . . . eliminate parentheses
an = 7n -5 . . . . . . . collect terms
