Find a4 for the arithmetic series with s4=-36 and a1=9

To find the value of a4 (the fourth term) in an arithmetic series, we need to use the given information of s4 (the sum of the first four terms) and a1 (the first term).

The formula for the sum of an arithmetic series is given by: Sn = (n/2)(a1 + an), where Sn represents the sum of the first n terms, a1 is the first term, and an is the last term.

In this case, we know that s4 is equal to -36, which means the sum of the first four terms is -36.

Plugging these values into the formula, we have: -36 = (4/2)(9 + a4).

Simplifying the equation, we get: -36 = 2(9 + a4).

Next, distribute 2 to both terms inside the parentheses: -36 = 18 +2a4.

To isolate a4, subtract 18 from both sides: -36 - 18 = 2a4.

Again, simplify: -54 = 2a4.

Finally, divide both sides by 2: -54/2 = a4.

Simplifying further, we have: a4 = -27.

Therefore, the fourth term (a4) in this arithmetic series is -27.