Answer :
Final answer:
To find the 28th term of the arithmetic sequence, we can use the given information to find the common difference (d) and the first term (a) of the sequence. Once we have these values, we can use the formula a + (n - 1)d to find the 28th term.
Explanation:
To find the 28th term of the arithmetic sequence, we need to determine the common difference (d) first. We can do this by finding the difference between two consecutive terms in the sequence. We are given that the sum of the first 7 terms is 63 and the sum of the next 7 terms is 161. Since there are 7 terms in each group, the sum of the first 7 terms can be written as:
7/2 * (2a + (7 - 1)d) = 63
Simplifying this equation gives us:
14a + 42d = 63
Similarly, the sum of the next 7 terms can be written as:
7/2 * (2(a + 7d) + (7 - 1)d) = 161
Simplifying this equation gives us:
14(a + 7d) + 42d = 161
We now have a system of two equations with two variables, a and d. By solving this system of equations, we can find the values of a and d. Once we have the values of a and d, we can find the 28th term of the arithmetic sequence using the formula:
a + (n - 1)d
