Answer:
b = 21
Explanation:
If there are 5 arithmetic means between 5 and b and the last term is 25, then we can find the value of b by using the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.
We know that there are 5 arithmetic means between 5 and b. Therefore, there are 7 terms in total (including 5 and b). We also know that the last term is 25. So we have:
a_7 = 25 a_1 = 5 n = 7
We can use these values to solve for d:
a_n = a_1 + (n - 1)d 25 = 5 + (7 - 1)d d = 4
Now that we know d, we can find b by using the formula for the fifth term:
a_5 = a_1 + (5 - 1)d a_5 = 5 + (4)(4) a_5 = 21
Therefore, b = 21.