Final answer:
To find the missing terms in an arithmetic sequence, calculate the common difference with the formula (last term - first term) / (number of terms - 1) and use this to determine each term using Tn = a + (n-1)d.
Step-by-step explanation:
To calculate the missing terms of each arithmetic sequence where the first and last terms are given, we use the formula for the nth term of an arithmetic sequence, which is:
Tn = a + (n-1)d, where 'a' is the first term, 'd' is the common difference, and n is the term number.
First, we calculate the common difference 'd' using the information given:
'd' = (last term - first term) / (number of terms - 1).
Then we can find each missing term using the formula Tn = a + (n-1)d.
For example, given an arithmetic sequence where the first term is 10 and the last term is 19, with total 4 terms:
d = (19 - 10) / (4 - 1) = 9 / 3 = 3.
So the sequence is 10, 13, 16, 19.