Subjects algebra

Ap Zero Term 54B6F2

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We are given an arithmetic progression (A.P.) with the first few terms 72, 68, 64, 60, … and we need to find which term is zero. 2. **Recall the formula for the nth term of an A.P.:** $$a_n = a_1 + (n-1)d$$ where $a_n$ is the nth term, $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number. 3. **Identify the known values:** - First term $a_1 = 72$ - Common difference $d = 68 - 72 = -4$ 4. **Set the nth term equal to zero and solve for $n$:** $$0 = 72 + (n-1)(-4)$$ 5. **Simplify the equation:** $$0 = 72 - 4(n-1)$$ $$4(n-1) = 72$$ $$n-1 = \frac{72}{4} = 18$$ $$n = 18 + 1 = 19$$ 6. **Interpretation:** The 19th term of the A.P. is zero. **Final answer:** The term of the A.P. that is zero is the 19th term.