The conversation between human and AI assistant.
What are some of the application problems in arithmetic progression?
How would you solve that one?
One way to solve it is to use the formula for the sum of an arithmetic progression: S_n = (n/2)*(a_1 + a_n), where S_n is the sum of the first n terms, and a_n is the nth term. We can plug in the known values from the problem to get 145 = (10/2)*(a_1 + a_10), which simplifies to 29 = a_1 + a_10. We also know that a_10 = a_1 + (10-1)3 = a_1 + 27. Substituting this into the previous equation gives 29 = a_1 + a_1 + 27, which simplifies to 2a_1 = 2, and therefore a_1 = 1.