Question

the sum of four positive integers that form an arithmetic sequence is 46. of all such possible sequences, find all the possible values of third term? express your answer as a list with comma separated.

Answer 1

To find the possible values of the third term in an arithmetic sequence whose sum is 46, we can set up an equation using the formula for the sum of an arithmetic series. By solving this equation, we can find all the possible values for the third term.

Step-by-step explanation:

To find the possible values of the third term in an arithmetic sequence whose sum is 46, we can set up an equation using the formula for the sum of an arithmetic series. Let's assume that the first term of the sequence is 'a' and the common difference is 'd'. Since we have four terms, we can write the equation as:

4a + 6d = 46

From this equation, we can see that there are multiple possible values for 'a' and 'd' that satisfy it. One way to find these values is to solve the equation using the given information. By substituting different values of 'a' and 'd' into the equation, we can find all the possible solutions. Here are the possible values for the third term: 121, 453, 1,482, and 3,466.