Question

Write a rule for the nth term of the sequence. Use your rule to find a30. –4, 5, 14, 23, 32, . . .

Answer 1

The nth term of the sequence – 4, 5, 14, 23, 32, ... follows the rule 9n - 13. To find the 30th term (a30), we calculate it as 9×30 - 13, which gives us a30 = 257.

Step-by-step explanation:

To write a rule for the nth term of the sequence: – 4, 5, 14, 23, 32, ..., you must first determine the pattern between each term. It can be observed that each term increases by 9 from the previous term, thus indicating a linear sequence. The first term of the sequence is – 4, and since each subsequent term increases by 9, the nth term of this sequence can be written as:

nth term = first term + (n - 1)×common difference

nth term = – 4 + (n - 1)×9

nth term = – 4 + 9n - 9

nth term = 9n - 13

Now to find the 30th term, a30, you simply plug in n = 30 into the rule:

a30 = 9×30 - 13

a30 = 270 - 13

a30 = 257

The 30th term of the given sequence is 257.

Answer 2

Step = 9
a30 = a1 + 9(30 - 1) = -4 + 9 × 29 = -4 + 261 = 267