Identifying Constant Difference in an Arithmetic Sequence
For the sequence 6, 9, 12, 15, …, determine if it is an arithmetic progression. If it is, state the value of the common difference and calculate the 9th term.
Part a
Formulate the equation for the sum of the first \(n\) terms for each arithmetic progression and state the relationship between these sums as given in the problem.
Part b
Solve the equation derived in part (a) under the condition that the common differences are equal, i.e., \(d_1 = d_2 = d\). Express \(a_1\) in terms of \(a_2\) and \(n\).