Determine whether each sequence is arithmetic or geometric. Find the next three items.
1. 14,19,24,29, . . .
a. geometric; 34, 39, 44
b. arithmetic; 32, 36, 41
c. arithmetic; 34, 39, 44
d. The sequence is neither geometric nor arithmetic.
add 5 to get the next terms.
To determine whether a sequence is arithmetic or geometric, we need to check the relationship between consecutive terms.
In the given sequence: 14, 19, 24, 29, ...
To check if it is an arithmetic sequence, we look for a common difference between consecutive terms. Here, the difference between each term is 5 (19 - 14 = 5, 24 - 19 = 5, and so on). Therefore, the sequence is arithmetic.
Now, to find the next three items in the sequence, we need to add the common difference to the last term of the sequence.
The last term of the sequence is 29. So, by adding the common difference of 5, we get:
Next term: 29 + 5 = 34
Second next term: 34 + 5 = 39
Third next term: 39 + 5 = 44
So, the next three items in the sequence are 34, 39, and 44.
Therefore, the correct answer is c. arithmetic; 34, 39, 44.