Write the explicit rule for the sequence:
2, 9, 16, 23, 30,…
question 2 options:
an=7n+2
an=7n−5
an=−7n−5
an=−7n+2

  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

sine

step-by-step explanation: