Question

* A formula modeling how to add finite sums in an arithmetic sequence is represented by the equation. S = (a + b), Express a in terms of b, s,and n.

Answer 1

SOLUTION:

Step 1 :

In this question, we are told that a formula modeling how to add finite sums in an arithmetic sequence is represented by the equation:

$S\text{ =}\frac{n}{2}(\text{ a + b )}$

Step 2:

We are meant to express a in terms of b, s, and n.

Then, we have that:

$\begin{gathered} S\text{ =}\frac{n}{2}\text{ ( a + b )} \\ \text{cross}-\text{ multiply, we have that:} \\ 2S\text{ = na + nb} \\ 2S\text{ - nb = na} \\ \text{Divide both sides by n, we have that:} \\ \frac{2S\text{ -nb}}{n}\text{ = a } \end{gathered}$

CONCLUSION:

$a\text{ = }\frac{2S\text{ - nb}}{n}$