Subjects algebra

8Th Term Ap

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1. **State the problem:** Find the 8th term of the arithmetic progression (A.P.) with the first three terms given as $-3, -1, 1$. 2. **Identify the formula:** The $n$th term of an A.P. is given by $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term and $d$ is the common difference. 3. **Find the common difference $d$:** Calculate $d$ by subtracting the first term from the second term: $$d = -1 - (-3) = -1 + 3 = 2$$ 4. **Apply the formula for the 8th term:** Substitute $a_1 = -3$, $d = 2$, and $n = 8$ into the formula: $$a_8 = -3 + (8-1) \times 2 = -3 + 7 \times 2 = -3 + 14 = 11$$ 5. **Conclusion:** The 8th term of the A.P. is $11$.